Fiducial marks for articles of manufacture with non-trivial dimensional variations

ABSTRACT

The illustrative embodiment of the present invention uses a tangible three-dimensional structure as a fiducial mark, which structure is, at least partially, tolerant of dimensional variations in the article. The illustrative embodiment uses three such tangible three-dimensional structures: (1) a portion of a tangible conical surface, (2) a portion of a tangible spheroidal surface, and (3) a portion of a tangible pyramidal surface.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. provisional PatentApplication Ser. No. 62/686,076, which is incorporated by reference forall purposes, but particularly for evincing possession of the claimedinventions.

This application is related to co-filed applications, which are alsoincorporated by reference:

-   U.S. patent application Ser. No. 16/014,741, entitled “Embedding    Fiducial Marks into Articles of Manufacture with Non-Trivial    Dimensional Variations”; and-   U.S. patent application Ser. No. 16/014,746, entitled “Registration    of Articles of Manufacture with Dimensional Variations”; and-   U.S. patent application Ser. No. 16/014,726, entitled “Systems of    Articles of Manufacture with Corresponding Fiducial Marks and    Dimensional Variations”.

FIELD OF THE INVENTION

The present invention relates to fiducial marks in general, and, inparticular, to fiducial marks for articles of manufacture that havesimilar, but not identical, shapes.

BACKGROUND OF THE INVENTION

Fiducial marks are widely using in manufacturing to enable an article ofmanufacture to be located or “registered.” For example, it is well knownin the prior art that the registration of a rigid article of manufacturecan be accomplished by establishing three non-collinear fiducialreference points in the coordinate system of the article. Each fiducialreference point is merely a mathematical abstraction, and, therefore, atangible representation of each fiducial reference point must be affixedto the article of manufacture. The tangible representation of a fiducialreference point is a fiducial mark.

After the fiducial marks are affixed to the article, the laterallocation and angular orientation of the article can be determined bylocating the fiducial reference marks. There are, however, disadvantageswith fiducial marks in the prior art.

BRIEF SUMMARY OF THE INVENTION

Some embodiments of the present invention enable an article ofmanufacture to be registered without some of the costs and disadvantagesfor doing so in the prior art. For example, when articles of manufacturehave non-trivial dimensional variations, the use of prior art fiducialmarks is often problematic. In particular, the dimensional variationscan cause a fiducial mark to be affixed to the article at a locationother than where it is intended to be. If a fiducial mark is not affixedwhere it is intended to be, then the fiducial mark misrepresents thelocation of its associated fiducial reference point. This, of course,hinders the proper registration of the article.

The illustrative embodiment of the present invention uses a tangiblethree-dimensional structure as a fiducial mark, which structure is, atleast partially, tolerant of dimensional variations in the article. Theillustrative embodiment uses three such tangible three-dimensionalstructures:

(1) a portion of a tangible conical surface,

(2) a portion of a tangible spheroidal surface, and

(3) a portion of a tangible pyramidal surface.

When the tangible representation of a fiducial reference point is aportion of a tangible conical surface, the location of the fiducialreference point is represented by the location of the apex of an(intangible) cone. Although there are an infinite number of cones withthe same apex, the spatial parameters of one (intangible) cone aredetermined. After the spatial parameters of the one (intangible) coneare determined, a hole is created in the material composing the articleof manufacture, which hole is defined, at least in part, by a portion ofa tangible conical surface. The spatial parameters of the tangibleconical surface correspond to the spatial parameters of the one(intangible) cone. The hole can be created, for example, by drillinginto the material with a drill bit that has, at least in part, a conicalcutting surface.

Thereafter, the location of the fiducial reference point (i.e., the apexof the cone) can be determined by probing the portion of the tangibleconical surface to determine its spatial parameters. After the spatialparameters of the portion of the tangible conical surface aredetermined, it is well known to those skilled in the art how todetermine the spatial parameters of the associated (intangible) cone.After the spatial parameters of the (intangible) cone are determined, itis well known to those skilled in the art how to determine the locationof the apex of the cone (i.e., the fiducial reference point).

Although variations in the dimensions of the article of manufacture canaffect the conical-surface area and conical-surface volume of thetangible conical surface, the variations do not affect the spatialparameters of the associated (intangible) cone. Therefore, variations inthe dimensions of the article do not affect the ability of the fiducialmark to accurately represent the location of the fiducial referencepoint.

When the tangible representation of a fiducial reference point is aportion of a tangible spheroidal surface, the location of the fiducialreference point is represented by the location of the center of a(intangible) spheroid. Although there are an infinite number ofspheroids with the same center, the spatial parameters of one(intangible) spheroid are determined. After the spatial parameters ofthe one (intangible) spheroid are determined, a hole is created in thematerial composing the article of manufacture, which hole is defined, atleast in part, by a portion of a tangible spheroidal surface. Thespatial parameters of the tangible spheroidal surface correspond to thespatial parameters of the one (intangible) spheroid. The hole can becreated, for example, by drilling into the material with a drill bitthat has, at least in part, a spheroidal cutting surface.

Thereafter, the location of the fiducial reference point (i.e., thecenter of the spheroid) can be determined by probing the portion of thetangible spheroidal surface to determine its spatial parameters. Afterthe spatial parameters of the portion of the tangible spheroidal surfaceare determined, it is well known to those skilled in the art how todetermine the spatial parameters of the associated (intangible)spheroid. After the spatial parameters of the (intangible) spheroid aredetermined, it is well known to those skilled in the art how todetermine the location of the center of the spheroid (i.e., the fiducialreference point).

Although variations in the dimensions of the article of manufacture canaffect the spheroidal-surface area and spheroidal-surface volume of thetangible spheroidal surface, the variations do not affect the spatialparameters of the associated (intangible) spheroid. Therefore,variations in the dimensions of the article do not affect the ability ofthe fiducial mark to accurately represent the location of the fiducialreference point.

When the tangible representation of a fiducial reference point is aportion of a tangible pyramidal surface, the location of the fiducialreference point is represented by the location of the apex of an(intangible) pyramid. Although there are an infinite number of pyramidswith the same apex, the spatial parameters of one (intangible) pyramidare determined. After the spatial parameters of the one (intangible)pyramid are determined, a hole is created in the material composing thearticle of manufacture, which hole is defined, at least in part, by aportion of a tangible pyramidal surface. The spatial parameters of thetangible pyramidal surface correspond to the spatial parameters of theone (intangible) pyramid. The hole can be created, for example, bymelting the material with a melting tip that has, at least in part, apyramidal melting surface.

Thereafter, the location of the fiducial reference point (i.e., the apexof the pyramid) can be determined by probing the portion of the tangiblepyramidal surface to determine its spatial parameters. After the spatialparameters of the portion of the tangible pyramidal surface aredetermined, it is well known to those skilled in the art how todetermine the spatial parameters of the associated (intangible) pyramid.After the spatial parameters of the (intangible) pyramid are determined,it is well known to those skilled in the art how to determine thelocation of the apex of the pyramid (i.e., the fiducial referencepoint).

Although variations in the dimensions of the article of manufacture canaffect the pyramidal-surface area and pyramidal-surface volume of thetangible pyramidal surface, the variations do not affect the spatialparameters of the associated (intangible) pyramid. Therefore, variationsin the dimensions of the article do not affect the ability of thefiducial mark to accurately represent the location of the fiducialreference point.

The illustrative embodiment of the present invention comprises:

-   -   a first hole in a first portion of a material composing the        article of manufacture, wherein the first hole in the first        portion of the material is defined, at least in part, by a first        portion of a first tangible conical surface, wherein the first        tangible conical surface establishes (i) a first conical apex,        and (ii) a first conical-surface volume;    -   a second hole in a second portion of the material composing the        article of manufacture, wherein the second hole in the second        portion of the material is defined, at least in part, by a        second portion of a second tangible conical surface, wherein the        second tangible conical surface establishes (i) a second conical        apex, and (ii) a second conical-surface volume; and    -   a third hole in a third portion of the material composing the        article of manufacture, wherein the third hole in the third        portion of the material is defined, at least in part, by a third        portion of a third tangible conical surface, wherein the third        tangible conical surface establishes (i) a third conical apex,        and (ii) a third conical-surface volume;    -   wherein the first conical apex, the second conical apex, and the        third conical apex are non-collinear; and    -   wherein the first conical-surface volume does not equal the        second conical-surface volume.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts an illustration of the salient components of additivemanufacturing system 100 in accordance with the illustrative embodimentsof the present invention.

FIG. 2 depicts an illustration of registration system 200 in accordancewith the illustrative embodiment of the present invention.

FIG. 3a depicts an orthogonal front view of conic drill bit 251 inaccordance with the illustrative embodiment of the present invention.

FIG. 3b depicts an orthogonal side view of conic drill bit 251 inaccordance with the illustrative embodiment of the present invention.

FIG. 3c depicts an orthogonal bottom view of conic drill bit 251 inaccordance with the illustrative embodiment of the present invention.

FIG. 4a depicts an orthogonal front view of spheroidal drill bit 252 inaccordance with the illustrative embodiment of the present invention.

FIG. 4b depicts an orthogonal side view of spheroidal drill bit 252 inaccordance with the illustrative embodiment of the present invention.

FIG. 4c depicts an orthogonal bottom view of spheroidal drill bit 252 inaccordance with the illustrative embodiment of the present invention.

FIG. 5a depicts an orthogonal front view of conic melting tip 253 inaccordance with the illustrative embodiment of the present invention.

FIG. 5b depicts an orthogonal side view of conic melting tip 253 inaccordance with the illustrative embodiment of the present invention.

FIG. 5c depicts an orthogonal bottom view of conic melting tip 253 inaccordance with the illustrative embodiment of the present invention.

FIG. 6a depicts an orthogonal front view of spheroidal melting tip 254in accordance with the illustrative embodiment of the present invention.

FIG. 6b depicts an orthogonal side view of spheroidal melting tip 254 inaccordance with the illustrative embodiment of the present invention.

FIG. 6c depicts an orthogonal bottom view of spheroidal melting tip 254in accordance with the illustrative embodiment of the present invention.

FIG. 7a depicts an orthogonal front view of pyramidal fiducial meltingtip 255 in accordance with the illustrative embodiment of the presentinvention.

FIG. 7b depicts an orthogonal side view of pyramidal fiducial meltingtip 255 in accordance with the illustrative embodiment of the presentinvention.

FIG. 7c depicts an orthogonal bottom view of pyramidal fiducial meltingtip 255 in accordance with the illustrative embodiment of the presentinvention.

FIG. 8a depicts an orthogonal front view of conic probe 256 inaccordance with the illustrative embodiment of the present invention.

FIG. 8b depicts an orthogonal side view of conic probe 256 in accordancewith the illustrative embodiment of the present invention.

FIG. 8c depicts an orthogonal bottom view of conic probe 256 inaccordance with the illustrative embodiment of the present invention.

FIG. 9a depicts an orthogonal front view of spheroidal probe 257 inaccordance with the illustrative embodiment of the present invention.

FIG. 9b depicts an orthogonal side view of spheroidal probe 257 inaccordance with the illustrative embodiment of the present invention.

FIG. 9c depicts an orthogonal bottom view of spheroidal probe 257 inaccordance with the illustrative embodiment of the present invention.

FIG. 10a depicts an orthogonal front view of pyramidal probe 258 inaccordance with the illustrative embodiment of the present invention.

FIG. 10b depicts an orthogonal side view of pyramidal probe 258 inaccordance with the illustrative embodiment of the present invention.

FIG. 10c depicts an orthogonal bottom view of pyramidal probe 258 inaccordance with the illustrative embodiment of the present invention.

FIG. 11 depicts a flowchart of the operation of the illustrativeembodiment of the present invention.

FIG. 12a depicts the orthogonal front view of the engineeringspecification for a first illustrative article of manufacture—solidhemisphere 1200.

FIG. 12b depicts the orthogonal side view of the engineeringspecification for a first illustrative article of manufacture—solidhemisphere 1200.

FIG. 12c depicts the orthogonal top view of the engineeringspecification for a first illustrative article of manufacture—solidhemisphere 1200.

FIG. 13a depicts the orthogonal front view of the engineeringspecification for a second illustrative article ofmanufacture—hemispherical shell 1300.

FIG. 13b depicts the orthogonal side view of the engineeringspecification for a second illustrative article ofmanufacture—hemispherical shell 1300.

FIG. 13c depicts the orthogonal top view of the engineeringspecification for a second illustrative article ofmanufacture—hemispherical shell 1300.

FIG. 14a depicts the orthogonal front view of solid hemisphere 1400,which was fabricated in accordance with the engineering specificationsdepicted in FIGS. 12a, 12b , and 12 c.

FIG. 14b depicts the orthogonal side view of solid hemisphere 1400,which was fabricated in accordance with the engineering specificationsdepicted in FIGS. 12a, 12b , and 12 c.

FIG. 14c depicts the orthogonal top view of solid hemisphere 1400, whichwas fabricated in accordance with the engineering specificationsdepicted in FIGS. 12a, 12b , and 12 c.

FIG. 15a depicts the orthogonal front view of solid hemisphere 1500,which was fabricated in accordance with the engineering specificationsdepicted in FIGS. 12a, 12b , and 12 c.

FIG. 15b depicts the orthogonal side view of solid hemisphere 1500,which was fabricated in accordance with the engineering specificationsdepicted in FIGS. 12a, 12b , and 12 c.

FIG. 15c depicts the orthogonal top view of solid hemisphere 1500, whichwas fabricated in accordance with the engineering specificationsdepicted in FIGS. 12a, 12b , and 12 c.

FIG. 16a depicts the orthogonal front view of hemispherical shell 1600,which was fabricated in accordance with the engineering specificationsdepicted in FIGS. 13a, 13b , and 13 c.

FIG. 16b depicts the orthogonal side view of hemispherical shell 1600,which was fabricated in accordance with the engineering specificationsdepicted in FIGS. 13a, 13b , and 13 c.

FIG. 16c depicts the orthogonal top view of hemispherical shell 1600,which was fabricated in accordance with the engineering specificationsdepicted in FIGS. 13a, 13b , and 13 c.

FIG. 17a depicts the orthogonal front view of hemispherical shell 1700,which was fabricated in accordance with the engineering specificationsdepicted in FIGS. 13a, 13b , and 13 c.

FIG. 17b depicts the orthogonal side view of hemispherical shell 1700,which was fabricated in accordance with the engineering specificationsdepicted in FIGS. 13a, 13b , and 13 c.

FIG. 17c depicts the orthogonal top view of hemispherical shell 1700,which was fabricated in accordance with the engineering specificationsdepicted in FIGS. 13a, 13b , and 13 c.

FIG. 18a depicts an orthogonal front view of conical blind hole 1800 inthermoplastic in accordance with the illustrative embodiment of thepresent invention.

FIG. 18b depicts an orthogonal side view of conical blind hole 1800 inthermoplastic in accordance with the illustrative embodiment of thepresent invention.

FIG. 18c depicts an orthogonal bottom view of conical blind hole 1800 inthermoplastic in accordance with the illustrative embodiment of thepresent invention.

FIG. 19a depicts an orthogonal front view of conical through hole 1900in thermoplastic in accordance with the illustrative embodiment of thepresent invention.

FIG. 19b depicts an orthogonal side view of conical through hole 1900 inthermoplastic in accordance with the illustrative embodiment of thepresent invention.

FIG. 19c depicts an orthogonal bottom view of conical through hole 1900in thermoplastic in accordance with the illustrative embodiment of thepresent invention.

FIG. 20a depicts an orthogonal front view of spheroidal blind hole 2000in thermoplastic in accordance with the illustrative embodiment of thepresent invention.

FIG. 20b depicts an orthogonal side view of spheroidal blind hole 2000in thermoplastic in accordance with the illustrative embodiment of thepresent invention.

FIG. 20c depicts an orthogonal bottom view of spheroidal blind hole 2000in thermoplastic in accordance with the illustrative embodiment of thepresent invention.

FIG. 21a depicts an orthogonal front view of spheroidal through hole2100 in thermoplastic in accordance with the illustrative embodiment ofthe present invention.

FIG. 21b depicts an orthogonal side view of spheroidal through hole 2100in thermoplastic in accordance with the illustrative embodiment of thepresent invention.

FIG. 21c depicts an orthogonal bottom view of spheroidal through hole2100 in thermoplastic in accordance with the illustrative embodiment ofthe present invention.

FIG. 22a depicts an orthogonal front view of pyramidal blind hole 2200in thermoplastic in accordance with the illustrative embodiment of thepresent invention.

FIG. 22b depicts an orthogonal side view of pyramidal blind hole 2200 inthermoplastic in accordance with the illustrative embodiment of thepresent invention.

FIG. 22c depicts an orthogonal bottom view of pyramidal blind hole 2200in thermoplastic in accordance with the illustrative embodiment of thepresent invention.

FIG. 23a depicts an orthogonal front view of pyramidal through hole 2300in thermoplastic in accordance with the illustrative embodiment of thepresent invention.

FIG. 23b depicts an orthogonal side view of pyramidal through hole 2300in thermoplastic in accordance with the illustrative embodiment of thepresent invention.

FIG. 23c depicts an orthogonal bottom view of pyramidal through hole2300 in thermoplastic in accordance with the illustrative embodiment ofthe present invention.

FIG. 24 depicts a flowchart of the salient tasks associated with theperformance of task 1103—imparting the representative fiducial marksinto the fabricated articles of manufacture.

FIG. 25 depicts a flowchart of the salient tasks associated with theperformance of task 1104—locating the first article of manufacture andthe second article of manufacture based on their representative fiducialmarks.

DETAILED DESCRIPTION

Axis of a Pyramid—For the purposes of this specification, the term “axisof a pyramid” is defined as a straight line that intersects the apex ofthe pyramid and that has a congruent angle between it and each lateraledge of the pyramid.

Bilateral Shape Similarity—For the purposes of this specification, theterm “bilateral shape similarity” of volume a with respect to volume bequals the harmonic mean of a # b and b # a. The bilateral shapesimilarity of volume a with respect to volume b is notated as a Δ b.

Blind Hole—For the purposes of this specification, the term “blind hole”is defined as hole in a material composing an article of manufacturethat is created to a specified depth without breaking through to theother side of the material.

Conical Apex—For the purposes of this specification, the term “conicalapex” is defined as a synonym of “the apex of a cone.”

Conical Fiducial Mark—For the purposes of this specification, the term“conical fiducial mark” is defined as hole in a material composing anarticle of manufacture, which hole is defined, at least in part, by aportion of a tangible conical surface.

Conical-Surface Area—For the purposes of this specification, the term“conical-surface area” is defined as the area of the portion of thetangible conical surface in the hole. Note that the area of the base ofthe cone is not included in the conical-surface area because the base ofthe cone is not represented by a tangible surface.

Conical-Surface Volume—For the purposes of this specification, the term“conical-surface volume” is defined as the volume of three-dimensionalspace that is surrounded by the portion of the tangible conical surfacein the hole.

Fiducial Reference Point—For the purposes of this specification, theterm “fiducial reference point” is defined a point in three-dimensionalspace.

Frustum of a Cone—For the purposes of this specification, the term“frustum of a cone” is defined as a portion of a cone cut off by aplane.

Frustum of a Pyramid—For the purposes of this specification, the term“frustum of a pyramid” is defined as a portion of a pyramid cut off by aplane.

Inferior Surface—For the purposes of this specification, the term“inferior surface” is defined as the surface of a material composing anarticle of manufacture through which the tool that creates arepresentative fiducial mark exits the material.

Pyramid—For the purposes of this specification, the term “pyramid” andits inflected form is defined as three or more triangular planar facesthat intersect at a single point, which point is the pyramidal apex.

Pyramidal Apex—For the purposes of this specification, the term“pyramidal apex” is defined as a the point at which three or moretriangular faces of a pyramid intersect. A “pyramidal apex” is a synonymof “the apex of a pyramid.”

Pyramidal Axis—For the purposes of this specification, the term“pyramidal axis” is a synonym of “axis of a pyramid.”

Pyramidal Fiducial Mark—For the purposes of this specification, the term“pyramidal fiducial mark” is defined as hole in a material composing anarticle of manufacture, which hole is defined, at least in part, by aportion of a tangible pyramidal surface.

Pyramidal-Surface Area—For the purposes of this specification, the term“pyramidal-surface area” is defined as the area of the portion of thetangible pyramidal surface in the hole. Note that the area of the baseof the pyramid is not included in the conical-surface area because thebase of the pyramid is not represented by a tangible surface.

Pyramidal-Surface Volume—For the purposes of this specification, theterm “pyramidal-surface volume” is defined as the volume ofthree-dimensional space that is surrounded by the portion of thetangible pyramidal surface in the hole.

Representative Fiducial Mark—For the purposes of this specification, theterm “representative fiducial mark” is defined as a three-dimensionalstructure that memorializes and establishes the location of a fiducialreference point in three-dimensional space. In accordance with theillustrative embodiment, there are three kinds of representativefiducial marks: (1) a tangible conical surface, (2) a tangiblespheroidal surface, and (3) a tangible pyramidal surface.

Spherical Cap—For the purposes of this specification, the term“spherical cap” is defined as a portion of a sphere cut off by a plane.

Spherical Segment—For the purposes of this specification, the term“spherical segment” is defined as a portion of a sphere that is cut offby two parallel planes.

Spheroidal Cap—For the purposes of this specification, the term“spheroidal cap” is defined as a portion of a spheroid cut off by aplane.

Spheroidal Fiducial Mark—For the purposes of this specification, theterm “spheroidal fiducial mark” is defined as hole in a materialcomposing an article of manufacture, which hole is defined, at least inpart, by a portion of a tangible spheroidal surface.

Spheroidal Segment—For the purposes of this specification, the term“spheroidal segment” is defined as a spheroid that is cut off by twoparallel planes.

Spheroidal-Surface Area—For the purposes of this specification, the term“spheroidal-surface area” is defined as the area of the portion of thetangible spheroidal surface in the hole.

Spheroidal-Surface Volume—For the purposes of this specification, theterm “spheroidal-surface volume” is defined as the volume ofthree-dimensional space that is surrounded by the portion of thetangible conical spheroidal in the hole.

Superior Surface—For the purposes of this specification, the term“superior surface” is defined as the surface of a material composing anarticle of manufacture into which the tool that creates a representativefiducial mark enters the material.

Tangible Conical Surface—For the purposes of this specification, theterm “tangible conical surface” is defined as a three-dimensionaltangible surface that establishes the spatial parameters of (i) a cone,(ii) conical apex, (iii) a conical axis, (iv) a conical-surface area,and (v) a conical-surface volume.

Tangible Pyramidal Surface—For the purposes of this specification, theterm “tangible pyramidal surface” is defined as a three-dimensionaltangible surface that establishes the spatial parameters of (i) apyramid, (ii) a pyramidal apex, (iii) a pyramidal axis, (iv) apyramidal-surface area, and (v) a pyramidal-surface volume.

Tangible Spheroidal Surface—For the purposes of this specification, theterm “tangible spheroidal surface” is defined as a three-dimensionaltangible surface that establishes the spatial parameters of (i) aspheroid, (ii) a center of the spheroid, (iii) a spheroidal axis ofsymmetry (for prolate spheroids and oblate spheroids), (iv) aspheroidal-surface area, and (v) a spheroidal-surface volume.

Through Hole—For the purposes of this specification, the term “throughhole” is defined as a hole in an article of manufacture that penetratesboth a superior surface and an inferior surface of the materialcomposing the article of manufacture.

Unilateral Shape Similarity—For the purposes of this specification, theterm “unilateral shape similarity” of volume a with respect to volume bis defined as the maximum percentage of volume a that can besuperimposed, without deformation, within volume b. The unilateral shapesimilarity of volume a with respect to volume b is notated as a # b.

FIG. 1 depicts an illustration of the salient components of additivemanufacturing system 100 in accordance with the illustrative embodimentsof the present invention. Additive manufacturing system 100 comprises:controller 101, build chamber 102, turntable 110, deposition build plate111, robot 121, deposition head 122, filament conditioning unit 129,filament source 130, and thermoplastic filament 131. The purpose ofmanufacturing system 100 is to fabricate article of manufacture 151(hereinafter “article 151”).

Controller 101 comprises the hardware and software necessary to directbuild chamber 102, robot 121, deposition head 122, and turntable 110, inorder to fabricate article 151. It will be clear to those skilled in theart how to make and use controller 101.

Build chamber 102 is a thermally-insulated, temperature-controlledenvironment in which article 151 is fabricated. It will be clear tothose skilled in art how to make and use build chamber 102.

Turntable 110 comprises a stepper motor—under the control of controller101—that is capable of rotating build plate 111 (and, consequentlyarticle 151) around the Z-axis (i.e., orthogonal to the build plate). Inparticular, turntable 110 is capable of:

-   -   i. rotating build plate 111 clockwise around the Z-axis from any        angle to any angle, and    -   ii. rotating build plate 111 counter-clockwise around the Z-axis        from any angle to any angle, and    -   iii. rotating build plate 111 at any rate, and    -   iv. maintaining (statically) the position of build plate 111 at        any angle.        It will be clear to those skilled in the art how to make and use        turntable 110.

Build plate 111 is a platform comprising hardware on which article 151is fabricated. Build plate 111 is configured to receive heated filamentdeposited by deposition head 122. It will be clear to those skilled inthe art how to make and use build plate 111.

Robot 121 is capable of depositing a segment of fiber-reinforcedthermoplastic filament from any three-dimensional coordinate in buildchamber 102 to any other three-dimensional coordinate in build chamber102 with deposition head 122 at any approach angle. To this end, robot121 comprises a multi-axis (e.g., six-axis, seven-axis, etc.),mechanical arm that is under the control of controller 101. Themechanical arm comprises first arm segment 123, second arm segment 124,and third arm segment 125. The joints between adjoining arm segments areunder the control of controller 101. A non-limiting example of robot 121is the IRB 4600 robot offered by ABB. It will be clear to those skilledin the art how to make and use robot 121.

The mechanical arm of robot 121 can move deposition head 122 in:

i. the +X direction,

ii. the −X direction,

iii. the +Y direction,

iv. the −Y direction,

v. the +Z direction,

vi. the −Z direction, and

vii. any combination of i, ii, iii, iv, v, and vi,

while rotating the approach angle of deposition head 122 around anypoint or temporal series of points. It will be clear to those skilled inthe art how to make and use robot 121.

Deposition head 122 comprises hardware that is under the control ofcontroller 101 and that deposits fiber-reinforced thermoplastic filament131. Deposition head 122 is described in detail in pending United Statespatent applications:

-   -   (i) Ser. No. 15/827,721, entitled “Filament Guide,” filed on        Nov. 30, 2017;    -   (ii) Ser. No. 15/827,711, entitled “Filament Heating in 3D        Printing Systems,” filed on Nov. 30, 2017;    -   (iii) Ser. No. 15/854,673, entitled “Alleviating Torsional        Forces on Fiber-Reinforced Thermoplastic Filament,” filed on        Dec. 26, 2017;    -   (iv) Ser. No. 15/854,676, entitled “Depositing Arced Portions of        Fiber-Reinforced Thermoplastic Filament,” filed Dec. 26, 2017;        all of which are incorporated by reference for the purpose of        describing additive manufacturing system 100 in general, and        deposition head 122 in particular.

Filament conditioning unit 129 comprises hardware that pre-heatsfilament 131 prior to deposition. It will be clear to those skilled inthe art how to make and use filament conditioning unit 129.

Filament 131 comprises a tow of reinforcing fibers that is substantiallyparallel to its longitudinal axis. In accordance with the illustrativeembodiments, filament 131 comprises a cylindrical towpreg of contiguous12K carbon fiber that is impregnated with thermoplastic resin.Thermoplastic filament 131 comprises contiguous carbon fiber, but itwill be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which thermoplastic filament 131 has a different fibercomposition.

It will be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which filament 131 comprises a different number of fibers(e.g., 1K, 3K, 6K, 24K, etc.). It will be clear to those skilled in theart, after reading this disclosure, how to make and use alternativeembodiments of the present invention in which the fibers in filament 131are made of a different material (e.g., fiberglass, aramid, carbonnanotubes, etc.).

In accordance with the illustrative embodiments, the thermoplastic is,in general, a semi-crystalline polymer and, in particular, thepolyaryletherketone (PAEK) known as polyetherketone (PEK). In accordancewith some alternative embodiments of the present invention, thesemi-crystalline material is the polyaryletherketone (PAEK),polyetheretherketone (PEEK), polyetherketoneketone (PEKK),polyetheretherketoneketone (PEEKK), or polyetherketoneetherketoneketone(PEKEKK). As those who are skilled in the art will appreciate afterreading this specification, the disclosed annealing process, as itpertains to a semi-crystalline polymer in general, takes place at atemperature that is above the glass transition temperature Tg.

In accordance with some alternative embodiments of the presentinvention, the semi-crystalline polymer is not a polyaryletherketone(PAEK) but another semi-crystalline thermoplastic (e.g., polyamide (PA),polybutylene terephthalate (PBT), poly(p-phenylene sulfide) (PPS), etc.)or a mixture of a semi-crystalline polymer and an amorphous polymer.

When the filament comprises a blend of an amorphous polymer with asemi-crystalline polymer, the semi-crystalline polymer can one of theaforementioned materials and the amorphous polymer can be apolyarylsulfone, such as polysulfone (PSU), polyethersulfone (PESU),polyphenylsulfone (PPSU), polyethersulfone (PES), or polyetherimide(PEI). In some additional embodiments, the amorphous polymer can be, forexample and without limitation, polyphenylene oxides (PPOs),acrylonitrile butadiene styrene (ABS), methyl methacrylate acrylonitrilebutadiene styrene copolymer (ABSi), polystyrene (PS), or polycarbonate(PC). As those who are skilled in the art will appreciate after readingthis specification, the disclosed annealing process, as it pertains to ablend of an amorphous polymer with a semi-crystalline polymer, takesplace generally at a lower temperature than a semi-crystalline polymerwith the same glass transition temperature; in some cases, the annealingprocess can take place at a temperature slightly below the glasstransition temperature.

When the filament comprises a blend of an amorphous polymer with asemi-crystalline polymer, the weight ratio of semi-crystalline materialto amorphous material can be in the range of about 50:50 to about 95:05,inclusive, or about 50:50 to about 90:10, inclusive. Preferably, theweight ratio of semi-crystalline material to amorphous material in theblend is between 60:40 and 80:20, inclusive. The ratio selected for anyparticular application may vary primarily as a function of the materialsused and the properties desired for the printed article.

In some alternative embodiment of the present invention, the filamentcomprises a metal. For example, and without limitation, the filament canbe a wire comprising stainless steel, Inconel® (nickel/chrome),titanium, aluminum, cobalt chrome, copper, bronze, iron, precious metals(e.g., platinum, gold, silver, etc.).

FIG. 2 depicts an illustration of registration system 200 in accordancewith the illustrative embodiment of the present invention. Registrationsystem 200 comprises: platform 201, robot mount and end-effector holder202, articulated robot arm 203, build-plate support 204, build plate205, end-effector chuck 207, end effector 208, and control station 209.Also shown in FIG. 2, but not a part of registration system 200, isregistration volume 206 and article of manufacture 211.

Platform 201 is a rigid structure that ensures that the relative spatialrelationship of robot mount and end-effector holder 202, articulatedrobot arm 203, end-effector chuck 207, and end effector 208 aremaintained and knowable with respect to build-plate support 204, buildplate 205, and article of manufacture 211. It will be clear to thoseskilled in the art how to make and use platform 201.

Robot mount and end-effector holder 202 is a rigid and stable supportfor articulated robot arm 203 and is readily-accessible storage for theend-effectors (e.g., conic drill bit 251, spheroidal drill bit 252,conic melting tip 253, spheroidal melting tip 254, pyramidal melting tip255, conical probe 256, spheroidal probe 257, pyramidal probe 258, etc.,which are described in detail below and in the accompanying figures)that are not currently in end-effector chuck 208. It will be clear tothose skilled in the art how to make and use robot mount andend-effector holder 202.

Articulated robot arm 203 is a six-axis robotic arm that comprises theactuators (e.g., motors, etc.), sensors, and electronics capable ofplacing the tip of end effector 208—under the command of control station209—at any location within registration volume 206 and from any approachangle. It will be clear to those skilled in the art how to makearticulated robot arm 203.

Build plate support 204 is a rigid and stable support for build plate205 and article of manufacture 211. Furthermore, build-plate support 204is capable of rotating build plate 205 (and with it article ofmanufacture 211) around the Z-axis from any angular position to anyangular position under the command of control station 209. The fact thatbuild-plate support 204 can rotate increases the number of options thatarticulated robot arm 203 has for placing the tip of end effector 208 atany location within registration volume 206 and from any approach angle.It will be clear to those skilled in the art how to make build-platesupport 204.

Build plate 205 is a rigid support onto which article of manufacture 211is affixed so that it cannot move or rotate. It will be clear to thoseskilled in the art how to make and use build plate 205.

Registration volume 206 is the region in three-dimensional space inwhich articulated robot arm 203 is capable of placing the tip of endeffector 208. Article of manufacture 211 exists completely withinregistration volume 206.

End-effector chuck 207 comprises the hardware to:

-   -   (i) pick up any end effector in end-effector storage 202, and    -   (ii) incorporate a fiducial reference point at any location in        registration volume 206 by removing a portion of article of        manufacture 211 by drilling a hole into article of manufacture        211 at any location from any approach angle with an end-effector        drill bit (e.g., conic drill bit 251, spheroidal drill bit 252,        etc.), and    -   (iii) incorporate a fiducial reference point at any location in        registration volume 206 by removing a portion of article of        manufacture 211 by melting a hole into article of manufacture        211 at any location from any approach angle with an end-effector        melting tip (e.g., conic melting tip 253, spheroidal melting tip        254, pyramidal melting tip 255, etc.), and    -   (iv) probe a hole at any location from any approach angle in        article of manufacture 211 to locate a fiducial reference point        with an end-effector probe (e.g., conic probe 256, spheroidal        probe 257, pyramidal probe 258, etc.), and    -   (v) store any end effector into end-effector storage 202.        It will be clear to those skilled in the art how to make and use        end-effector chuck 207.

End effector 208 is an article of manufacture that is capable of eitherincorporating a fiducial reference point at a specific location inarticle of manufacture 211 or of locating a fiducial reference point inarticle of manufacture 211. In accordance with the illustrativeembodiment, there are eight end effectors—five for incorporating afiducial reference point and three for locating a fiducial referencepoint. The five end effectors for incorporating fiducial referencepoints are:

(i) conic drill bit 251, and

(ii) spheroidal drill bit 252, and

(iii) conic melting tip 253, and

(iv) spheroidal melting tip 254, and

(v) pyramidal melting tip 255.

Each of these is described below and in the accompanying figures. Thethree end effectors for locating fiducial reference points are:

(i) conical probe 256, and

(ii) spheroidal probe 257, and

(iii) pyramidal probe 258.

Each of these eight end effectors is described below and in theaccompanying figures.

Control station 209 comprises the hardware and software necessary tooperate registration system 200. It will be clear to those skilled inthe art, after reading this disclosure, how to make and use controlstation 209.

FIGS. 3a, 3b, and 3c depict the orthogonal front, side, and bottomviews, respectively, of conic drill bit 251 in accordance with theillustrative embodiment of the present invention.

Conic drill bit 251 is used by the illustrative embodiment to establisha fiducial reference point at a location in the coordinate system of anarticle of manufacture. In accordance with the illustrative embodiment,the fiducial reference point can be:

-   -   (i) on the surface of the material composing the article of        manufacture, or    -   (ii) within (i.e., buried) the material composing the article of        manufacture (when using a frustum of a conic drill bit), or    -   (iii) outside the material composing the article of manufacture        with no tangible connection to the article of manufacture.

When conic drill bit 251 is used to establish a fiducial referencepoint, the fiducial reference point is represented by the apex of a cone(also herein called a “conical apex”). It is well known to those skilledin the art that a conical apex—like a fiducial reference point—is ageometric point.

In accordance with the illustrative embodiment, conic drill bit 251establishes a fiducial reference point (i.e., the conical apex) at alocation in the coordinate system of the article of manufacture bydrilling a hole into the material that composes the article ofmanufacture, wherein the hole is defined, at least in part, by a portionof a tangible conical surface.

Thereafter, the location of the apex of the cone (i.e., the fiducialreference point) can be determined by probing the portion of thetangible conical surface to determine its spatial parameters. After thespatial parameters of the portion of the tangible conical surface aredetermined, it is well known to those skilled in the art how todetermine the spatial parameters of the associated cone. After thespatial parameters of the cone are determined, it is well known to thoseskilled in the art how to determine the location of the apex of the cone(i.e., the fiducial reference point). A probe that is specificallydesigned for probing the portion of the tangible conical surface anddetermining its spatial parameters is described below and in theaccompanying figures.

Referring again to FIGS. 3a, 3b, and 3c , conic drill bit 251 comprisesa shank, a body, and a cutting surface.

In accordance with the illustrative embodiment, conic drill bit 251 isfabricated out of tungsten carbide, but it will be clear to thoseskilled in the art how to make and use alternative embodiments of thepresent invention in which a conic drill bit is fabricated out ofanother material or materials.

In accordance with the illustrative embodiment, the shank of conic drillbit 251 has a length of 2 cm and a diameter of 1 cm It will be clear tothose skilled in the art how to make and use alternative embodiments ofthe present invention in which the shank has different dimensions.

In accordance with the illustrative embodiment, the body of conic drillbit 251 has a length of 3 cm and a diameter of 3 cm. It will be clear tothose skilled in the art how to make and use alternative embodiments ofthe present invention in which the body has different dimensions.

In accordance with the illustrative embodiment, the cutting surface ofconic drill bit 251 is a right-circular cone with an drill point angle(i.e., apex angle) of π/3 radians (i.e., 60°). The axis of theright-circular cone of the cutting surface is collinear with the axis ofrotation of conic drill bit 251. In addition, the cutting surface ofconic drill bit 251 comprises four equally-spaced flutes. It will beclear to those skilled in the art, after reading this disclosure, how tomake and use alternative embodiments of the present invention in whichthe cutting surface of a conic drill bit has any “apex angle” or “drillpoint angle (e.g., π/6 radians, π/4 radians, etc.) and any number offlutes.

It will also be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which the cutting surface of a conic drill bit comprisesonly the frustum of a cone, with or without a pilot like used withspheroidal drill bit 252. When, for example, a frustum-of-a-cone drillbit is used to drill a blind hole into the material composing an articleof manufacture, the apex of the cone can be buried within the materialor, alternatively, outside the inferior surface.

Conic drill bit 251 is capable of drilling a “blind” hole into thematerial (e.g., thermoplastic, fiber-reinforced thermoplastic,thermoset, fiber-reinforced thermoset, metal, glass, ceramic, composite,etc.) composing the article of manufacture such that the blind hole isdefined, at least in part, by a portion of a tangible conical surface.FIGS. 18a, 18b, and 18c depict a blind hole—conic blind hole 1800—thatis defined by a portion of a tangible conical surface.

Conic drill bit 251 is also capable of drilling a “through” hole intothe material (e.g., thermoplastic, fiber-reinforced thermoplastic,thermoset, fiber-reinforced thermoset, metal, glass, ceramic, composite,etc.) composing the article of manufacture such that the through hole isdefined, at least in part, by a portion of a tangible conical surface.FIGS. 19a, 19b, and 19c depict a through hole—conic through hole1900—that is defined by a portion of a tangible conical surface.

In accordance with the illustrative embodiment—although it is notpossible in every instance—the portion of the tangible conical surfaceis advantageously embedded so that the conical axis passes through thefiducial reference point and is normal to the superior surface. It willbe clear to those skilled in the art, after reading this disclosure, howto make and use alternative embodiments of the present invention inwhich the conical axis has any relationship to the superior surface (andinferior surface, if any).

In accordance with the illustrative embodiment, each conic blind holeand each conic through hole is characterized by two metrics:

(i) the “conical-surface area,” and

(ii) the “conical-surface volume.”

The conical-surface area and the conical-surface volume can be, but arenot necessarily, related to:

(i) the amount of material removed to create the hole, or

(ii) the contour of the superior surface before or after the hole iscreated, or

(iii) the contour of the inferior surface (if any) before or after thehole is created.

For the purposes of this specification, the term “conical-surface area”is defined as the area of the portion of the tangible conical surface inthe hole. For example, when the superior surface is planar and theconical axis is normal to the superior surface, the conical-surface areaS of the conic blind hole equals:S=πR(R+√{square root over (h ² +R ²)})  (Eq. 1)where R is the radius of the cone at the superior surface and h is thedistance from the apex to the plane containing the superior surface. Asanother example, when the superior and inferior surfaces are planar andparallel and the conical axis is normal to the superior surface, theconical-surface area S of the conic through hole equals:S=π(R+r)√{square root over ((R+r)² +h ²)}(Eq. 2)where R is the radius of the cone at the superior surface, r is theradius of the cone at the inferior surface, and h is the normal distancefrom the plane containing the inferior surface to the plane containingthe superior surface. It will be clear to those skilled in the art howto calculate (analytically or numerically) and measure empirically theconical-surface area of any conic blind hole and any conic through hole.

For the purposes of this specification, the term “conical-surfacevolume” is defined as the volume of three-dimensional space that issurrounded by the portion of the tangible conical surface in the hole.For example, when the superior surface is planar and the conical axis isnormal to the superior surface, the conical-surface volume V of theconic blind hole equals:

$\begin{matrix}{V = \frac{\pi\;{hR}^{2}}{3}} & \left( {{Eq}.\mspace{14mu} 3} \right)\end{matrix}$where R is the radius of the cone at the superior surface and h is thedistance from the apex to the plane containing the superior surface. Asanother example, when the superior and inferior surfaces are planar andparallel and the conical axis is normal to the superior surface, theconical-surface volume V of the conic through hole equals:

$\begin{matrix}{V = {\frac{\pi\; h}{3}\left( {R^{2} + r^{2} + {R*r}} \right)}} & \left( {{Eq}.\mspace{14mu} 4} \right)\end{matrix}$where R is the radius of the cone at the superior surface, r is theradius of the cone at the inferior surface, and h is the normal distancefrom the plane containing the inferior surface to the plane containingthe superior surface. It will be clear to those skilled in the art howto calculate (analytically or numerically) and measure empirically thevolume of any conic blind hole and any conic through hole.

In accordance with the illustrative embodiment it is expected thatvariations in manufacturing will cause variations in the mass, volume,and dimensions of fabricated articles of manufacture that, in turn, willlead to:

-   -   (i) variations in the conical-surface volumes of the conical        holes (blind and through) in a single article of manufacture,        and    -   (ii) variations in the conical-surface volumes of corresponding        conical holes (blind and through) in corresponding articles of        manufacture, and    -   (iii) variations in the conical-surface areas of the conical        holes (blind and through) in a single article of manufacture,        and    -   (ii) variations in the conical-surface areas of corresponding        conical holes (blind and through) in corresponding articles of        manufacture.

In accordance with the illustrative embodiment, the material composingan article of manufacture comprises:

(i) one, two, three, four, or more conic blind holes, or

(ii) one, two, three, four, or more conic through holes, or

(iii) any combination of i and ii.

It will be clear to those skilled in the art, after reading thisdisclosure, how to make and use conic drill bit 251.

FIGS. 4a, 4b, and 4c depict the orthogonal front, side, and bottomviews, respectively, of spheroidal drill bit 252 in accordance with theillustrative embodiment of the present invention.

Spheroidal drill bit 252 is used by the illustrative embodiment toestablish a fiducial reference point at a location in the coordinatesystem of an article of manufacture. In accordance with the illustrativeembodiment, the fiducial reference point can be:

-   -   (i) on the surface of the material composing the article of        manufacture, or    -   (ii) within (i.e., buried) the material composing the article of        manufacture (when using a frustum of a spheroidal drill bit), or    -   (iii) outside the material composing the article of manufacture        with no tangible connection to the article of manufacture.

When spheroidal drill bit 252 is used to establish a fiducial referencepoint, the fiducial reference point is represented by the center of aspheroid. It is well known to those skilled in the art that the centerof a spheroid—like a fiducial reference point—is a geometric point.

In accordance with the illustrative embodiment, spheroidal drill bit 252establishes a fiducial reference point (i.e., the center of a spheroid)at a location in the coordinate system of the article of manufacture bydrilling a hole into the material that composes the article ofmanufacture, wherein the hole is defined, at least in part, by a portionof a tangible spheroidal surface.

Thereafter, the location of the center of the spheroid (i.e., thefiducial reference point) can be determined by probing the portion ofthe tangible spheroidal surface to determine its spatial parameters.After the spatial parameters of the portion of the tangible spheroidalsurface are determined, it is well known to those skilled in the art howto determine the spatial parameters of the associated spheroid. Afterthe spatial parameters of the spheroid are determined, it is well knownto those skilled in the art how to determine the location of the centerof the spheroid (i.e., the fiducial reference point). A probe that isspecifically designed for probing the portion of the tangible spheroidalsurface and determining its spatial parameters is described below and inthe accompanying figures.

Referring again to FIGS. 4a, 4b, and 4c , spheroidal drill bit 252comprises a shank, a body, a cutting surface, and a pilot.

In accordance with the illustrative embodiment, spheroidal drill bit 252is fabricated out of tungsten carbide, but it will be clear to thoseskilled in the art how to make and use alternative embodiments of thepresent invention in which a spheroidal drill bit is fabricated out ofanother material or materials.

In accordance with the illustrative embodiment, the shank of spheroidaldrill bit 252 has a length of 2 cm and a diameter of 1 cm It will beclear to those skilled in the art how to make and use alternativeembodiments of the present invention in which the shank has differentdimensions.

In accordance with the illustrative embodiment, the body of spheroidaldrill bit 252 has a length of 3 cm and a diameter of 3 cm. It will beclear to those skilled in the art how to make and use alternativeembodiments of the present invention in which the body has differentdimensions.

In accordance with the illustrative embodiment, the cutting surface ofspheroidal drill bit 252 is a hemisphere (i.e., one half of a sphere)with a radius of 1.5 cm. It will be clear to those skilled in the art,however, after reading this disclosure, how to make and use alternativeembodiments of the present invention in which a spheroidal drill bit hasa cutting surface that cuts a portion of any tangible spheroidal surface(e.g., a prolate spheroid, an oblate spheroid, a sphere). The axis ofrotation of spheroidal drill bit 252 is collinear with the axis ofsymmetry of the spheroid and intersects the center of the sphere. Inaddition, the cutting surface of spheroidal drill bit 252 comprises fourequally-spaced flutes. It will be clear to those skilled in the art,after reading this disclosure, how to make and use alternativeembodiments of the present invention in which the cutting surface of aspheroidal drill bit has any spheroidal size and shape and any number offlutes.

In accordance with the illustrative embodiment, spheroidal drill bit 252comprises a 1 cm pilot drill bit that assists in drilling. It will beclear to those skilled in the art, after reading this disclosure, how tomake and use alternative spheroidal drill bits that do not comprise apilot.

It will also be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which the cutting surface of a spheroidal drill bitcomprises only the frustum of a spheroid (with or without a pilot).

Spheroidal drill bit 252 is capable of drilling a “blind” hole into thematerial (e.g., thermoplastic, fiber-reinforced thermoplastic,thermoset, fiber-reinforced thermoset, metal, glass, ceramic, composite,etc.) composing the article of manufacture such that the blind hole isdefined, at least in part, by a portion of a tangible spheroidalsurface. FIGS. 20a, 20b, and 20c depict a blind hole—spheroidal blindhole 2000—that is defined by a portion of a tangible spheroidal surface.

Spheroidal drill bit 252 is also capable of drilling a “through” holeinto the material (e.g., thermoplastic, fiber-reinforced thermoplastic,thermoset, fiber-reinforced thermoset, metal, glass, ceramic, composite,etc.) composing the article of manufacture such that the through hole isdefined, at least in part, by a portion of a tangible spheroidalsurface. FIGS. 21a, 22b, and 23c depict a through hole—spheroidalthrough hole 2100—that is defined by a portion of a tangible spheroidalsurface.

In accordance with the illustrative embodiment—although it is notpossible in every instance—the portion of the tangible spheroidalsurface is advantageously embedded so that the spheroidal axis ofsymmetry passes through the fiducial reference point and is normal tothe superior surface. It will be clear to those skilled in the art thata prolate spheroid and an oblate spheroid have exactly one spheroidalaxis of symmetry and that a sphere has an infinite number of spheroidalaxes of symmetry. Furthermore, it will be clear to those skilled in theart, after reading this disclosure, how to make and use alternativeembodiments of the present invention in which the spheroidal axis ofsymmetry passes through the fiducial reference point and has anyrelationship to the superior surface (and inferior surface, if any).

In accordance with the illustrative embodiment, each spherical blindhole and each spherical through hole is characterized by two metrics:

(i) the “spheroidal-surface area,” and

(ii) the “spheroidal-surface volume.”

The spheroidal-surface area and the spheroidal-surface volume can be,but are not necessarily, related to:

(i) the amount of material removed to create the hole, or

(ii) the contour of the superior surface before or after the hole iscreated, or

(iii) the contour of the inferior surface (if any) before or after thehole is created.

For the purposes of this specification, the term “spheroidal-surfacearea” is defined as the area of the portion of the tangible spheroidalsurface in the hole. For example, when the superior surface is planarand the spheroidal axis of symmetry of the hole is normal to thesuperior surface, the spheroidal-surface area S of the spheroidal blindhole equals:S=2πRh  (Eq. 5)where R is the radius of the circle intersected by the superior surfaceand h is the radius R minus the distance from the apex to the planecontaining the superior surface. As another example, when the superiorand inferior surfaces are planar and parallel and the spheroidal axis ofsymmetry of the hole is normal to the superior surface, thespheroidal-surface area S of a spheroidal through hole equals:S=2πRc  (Eq. 6)where R is the radius of the circle intersected by the superior surface,and c is the normal distance from the plane containing the inferiorsurface to the plane containing the superior surface. It will be clearto those skilled in the art how to calculate (analytically ornumerically) and measure empirically the spheroidal-surface area of anyspheroidal blind hole and any spheroidal through hole.

For the purposes of this specification, the term “spheroidal-surfacevolume” is defined as the volume of three-dimensional space that issurrounded by the portion of the tangible spheroidal surface in thehole. For example, when the superior surface is planar and the spheroidis a sphere, the spheroidal-surface volume V of a spheroidal blind holeequals:

$\begin{matrix}{V = {\frac{\pi\; h}{6}\left( {{3\; a^{2}} + h^{2}} \right)}} & \left( {{Eq}.\mspace{14mu} 7} \right)\end{matrix}$where a is the radius of the circle intersected by the superior surfaceand h equals the radius of the sphere r minus the distance from centerof the sphere to the plane containing the superior surface. As anotherexample, when the superior and inferior surfaces are planar and paralleland the spheroid is a sphere, the spheroidal-surface volume V of aspheroidal through hole equals:

$\begin{matrix}{V = {\frac{\pi\; h}{6}\left( {{3\; a^{2}} + {3\; b^{2}} + h^{2}} \right)}} & \left( {{Eq}.\mspace{14mu} 8} \right)\end{matrix}$where a is the radius of the circle intersected by the superior surface,b is the radius of the circle intersected by the inferior surface, and his the normal distance from the plane containing the inferior surface tothe plane containing the superior surface. It will be clear to thoseskilled in the art how to calculate (analytically or numerically) andmeasure empirically the spheroidal-surface volume of any spheroidalblind hole and any spheroidal through hole.

In accordance with the illustrative embodiment it is expected thatvariations in manufacturing will cause variations in the mass, volume,and dimensions of fabricated articles of manufacture that, in turn, willlead to:

-   -   (i) variations in the spheroidal-surface volumes of the        spheroidal holes (blind and through) in a single article of        manufacture, and    -   (ii) variations in the spheroidal-surface volumes of        corresponding spheroidal holes (blind and through) in        corresponding articles of manufacture, and    -   (iii) variations in the spheroidal-surface areas of the        spheroidal holes (blind and through) in a single article of        manufacture, and    -   (ii) variations in the spheroidal-surface areas of corresponding        spheroidal holes (blind and through) in corresponding articles        of manufacture.

In accordance with the illustrative embodiment, the material composingan article of manufacture comprises:

(i) one, two, three, four, or more spheroidal blind holes, or

(ii) one, two, three, four, or more spheroidal through holes, or

(iii) any combination of i and ii.

It will be clear to those skilled in the art, after reading thisdisclosure, how to make and use spheroidal drill bit 252.

FIGS. 5a, 5b, and 5c depict the orthogonal front, side, and bottomviews, respectively, of conic melting tip 253 in accordance with theillustrative embodiment of the present invention.

Conic melting tip 253 is used by the illustrative embodiment toestablish a fiducial reference point at a location in the coordinatesystem of an article of manufacture. In accordance with the illustrativeembodiment, the fiducial reference point can be:

-   -   (i) on the surface of the material composing the article of        manufacture, or    -   (ii) within (i.e., buried) the material composing the article of        manufacture (when using a frustum of a conic melting tip), or    -   (iii) outside the material composing the article of manufacture        with no tangible connection to the article of manufacture.

When conic melting tip 253 is used to establish a fiducial referencepoint, the fiducial reference point is represented by the apex of a cone(also herein called “a conical apex”). It is well known to those skilledin the art that a conical apex—like a fiducial reference point—is ageometric point.

In accordance with the illustrative embodiment, conic melting tip 253establishes a fiducial reference point (i.e., the conical apex) at alocation in the coordinate system of the article of manufacture bymelting a hole into the material that composes the article ofmanufacture, wherein the hole is defined, at least in part, by a portionof a tangible conical surface.

Thereafter, the location of the apex of the cone (i.e., the fiducialreference point) can be determined by probing the portion of thetangible conical surface to determine its spatial parameters. After thespatial parameters of the portion of the tangible conical surface aredetermined, it is well known to those skilled in the art how todetermine the spatial parameters of the associated cone. After thespatial parameters of the cone are determined, it is well known to thoseskilled in the art how to determine the location of the apex of the cone(i.e., the fiducial reference point). A probe that is specificallydesigned for probing the portion of the tangible conical surface anddetermining its spatial parameters is described below and in theaccompanying figures.

Referring again to FIGS. 5a, 5b, and 5c , conic melting tip 253comprises a shank, a body, and a melting surface.

In accordance with the illustrative embodiment, conic drill bit 251 isfabricated out of steel, but it will be clear to those skilled in theart how to make and use alternative embodiments of the present inventionin which a conic drill bit is fabricated out of another material ormaterials.

In accordance with the illustrative embodiment, the shank of conicmelting tip 253 has a length of 2 cm and a diameter of 1 cm It will beclear to those skilled in the art how to make and use alternativeembodiments of the present invention in which the shank has differentdimensions.

In accordance with the illustrative embodiment, the body of conicmelting tip 253 has a length of 3 cm and a diameter of 3 cm. It will beclear to those skilled in the art how to make and use alternativeembodiments of the present invention in which the body has differentdimensions.

In accordance with the illustrative embodiment, the melting surface ofconic melting tip 253 is a right-circular cone with an apex angle of π/3radians (i.e., 60°). The axis of the right-circular cone of the meltingsurface is collinear with the axis of conic melting tip 253. It will beclear to those skilled in the art, after reading this disclosure, how tomake and use alternative embodiments of the present invention in whichthe melting surface of a conic melt tip has any apex angle.

It will also be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which the melting surface of a conic melting tip comprisesonly the frustum of a cone. When, for example, a frustum-of-a-conemelting tip is used to drill a blind hole into the material composing anarticle of manufacture, the apex of the cone can be buried within thematerial or, alternatively, outside the inferior surface.

Conic melting tip 253 is capable of drilling a “blind” hole into thematerial (e.g., thermoplastic, fiber-reinforced thermoplastic,thermoset, fiber-reinforced thermoset, metal, glass, ceramic, composite,etc.) composing the article of manufacture such that the blind hole isdefined, at least in part, by a portion of a tangible conical surface.FIGS. 18a, 18b, and 18c depict a blind hole—conic blind hole 1800—thatis defined by a portion of a tangible conical surface.

Conic melting tip 253 is also capable of drilling a “through” hole intothe material (e.g., thermoplastic, fiber-reinforced thermoplastic,thermoset, fiber-reinforced thermoset, metal, glass, ceramic, composite,etc.) composing the article of manufacture such that the through hole isdefined, at least in part, by a portion of a tangible conical surface.FIGS. 19a, 19b, and 19c depict a through hole—conic through hole1900—that is defined by a portion of a tangible conical surface.

In accordance with the illustrative embodiment—although it is notpossible in every instance—the portion of the tangible conical surfaceis advantageously embedded so that the conical axis passes through thefiducial reference point and is normal to the superior surface. It willbe clear to those skilled in the art, after reading this disclosure, howto make and use alternative embodiments of the present invention inwhich the conical axis has any relationship to the superior surface (andinferior surface, if any).

It will be clear to those skilled in the art, after reading thisdisclosure, how to make and use melting tip 253.

FIGS. 6a, 6b, and 6c depict the orthogonal front, side, and bottomviews, respectively, of spheroidal melting tip 254 in accordance withthe illustrative embodiment of the present invention.

Spheroidal melting tip 254 is used by the illustrative embodiment toestablish a fiducial reference point at a location in the coordinatesystem of an article of manufacture. In accordance with the illustrativeembodiment, the fiducial reference point can be:

-   -   (i) on the surface of the material composing the article of        manufacture, or    -   (ii) within (i.e., buried) the material composing the article of        manufacture (when using a frustum of a spheroidal melting tip),        or    -   (iii) outside the material composing the article of manufacture        with no tangible connection to the article of manufacture.

When spheroidal melting tip 254 is used to establish a fiducialreference point, the fiducial reference point is represented by thecenter of a spheroid. It is well known to those skilled in the art thatthe center of a spheroid—like a fiducial reference point—is a geometricpoint.

In accordance with the illustrative embodiment, spheroidal melting tip254 establishes a fiducial reference point (i.e., the center of aspheroid) at a location in the coordinate system of the article ofmanufacture by melting a hole into the material that composes thearticle of manufacture, wherein the hole is defined, at least in part,by a portion of a tangible spheroidal surface.

Thereafter, the location of the center of the spheroid (i.e., thefiducial reference point) can be determined by probing the portion ofthe tangible spheroidal surface to determine its spatial parameters.After the spatial parameters of the portion of the tangible spheroidalsurface are determined, it is well known to those skilled in the art howto determine the spatial parameters of the associated spheroid. Afterthe spatial parameters of the spheroid are determined, it is well knownto those skilled in the art how to determine the location of the centerof the spheroid (i.e., the fiducial reference point). A probe that isspecifically designed for probing the portion of the tangible spheroidalsurface and determining its spatial parameters is described below and inthe accompanying figures.

Referring again to FIGS. 6a, 6b, and 6c , spheroidal melting tip 254comprises a shank, a body, a spheroidal melting surface, and a pilot.

In accordance with the illustrative embodiment, spheroidal melting tip254 is fabricated out of steel, but it will be clear to those skilled inthe art how to make and use alternative embodiments of the presentinvention in which a spheroidal melting tip is fabricated out of anothermaterial or materials.

In accordance with the illustrative embodiment, the shank of spheroidalmelting tip 254 has a length of 2 cm and a diameter of 1 cm It will beclear to those skilled in the art how to make and use alternativeembodiments of the present invention in which the shank has differentdimensions.

In accordance with the illustrative embodiment, the body of spheroidalmelting tip 254 has a length of 3 cm and a diameter of 3 cm. It will beclear to those skilled in the art how to make and use alternativeembodiments of the present invention in which the body has differentdimensions.

In accordance with the illustrative embodiment, the melting surface ofspheroidal melting tip 254 hemisphere (i.e., one half of a sphere) witha radius of 1.5 cm. It will be clear to those skilled in the art,however, after reading this disclosure, how to make and use alternativeembodiments of the present invention in which a spheroidal melting tiphas a melting surface that is one-half of any spheroid (e.g., a prolatespheroid, an oblate spheroid, a sphere). The axis of the shank and bodyof spheroidal melting tip 254 intersects the center of the spheroid. Itwill be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which the melting surface of a spheroidal melt tip has anyradius.

In accordance with the illustrative embodiment, spheroidal melting tip254 comprises a pilot melting tip that assists in melting. It will beclear to those skilled in the art, after reading this disclosure, how tomake and use alternative spheroidal melting tips that do not comprise apilot.

It will also be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which the melting surface of a spheroidal melting tipcomprises only the frustum of a sphere (with or without a pilot).

Spheroidal melting tip 254 is capable of melting a “blind” hole into thematerial (e.g., thermoplastic, fiber-reinforced thermoplastic,thermoset, fiber-reinforced thermoset, metal, glass, ceramic, composite,etc.) composing the article of manufacture such that the blind hole isdefined, at least in part, by a portion of a tangible spheroidalsurface. FIGS. 20a, 20b, and 20c depict a blind hole—spheroidal blindhole 2000—that is defined by a portion of a tangible spheroidal surface.

Spheroidal melting tip 254 is also capable of melting a “through” holeinto the material (e.g., thermoplastic, fiber-reinforced thermoplastic,thermoset, fiber-reinforced thermoset, metal, glass, ceramic, composite,etc.) composing the article of manufacture such that the through hole isdefined, at least in part, by a portion of a tangible spheroidalsurface. FIGS. 21a, 22b, and 23c depict a through hole—spheroidalthrough hole 2100—that is defined by a portion of a tangible spheroidalsurface.

In accordance with the illustrative embodiment—although it is notpossible in every instance—the portion of the tangible spheroidalsurface is advantageously embedded so that the spheroidal axis ofsymmetry passes through the fiducial reference point and is normal tothe superior surface. It will be clear to those skilled in the art thata prolate spheroid and an oblate spheroid have exactly one spheroidalaxis of symmetry and that a sphere has an infinite number of spheroidalaxes of symmetry. Furthermore, it will be clear to those skilled in theart, after reading this disclosure, how to make and use alternativeembodiments of the present invention in which the spheroidal axis ofsymmetry passes through the fiducial reference point and has anyrelationship to the superior surface (and inferior surface, if any).

It will be clear to those skilled in the art, after reading thisdisclosure, how to make and use spheroidal melting tip 254.

FIGS. 7a, 7b, and 7c depict the orthogonal front, side, and bottomviews, respectively, of pyramidal melting tip 255 in accordance with theillustrative embodiment of the present invention.

Pyramidal melting tip 255 is used by the illustrative embodiment toestablish a fiducial reference point at a location in the coordinatesystem of an article of manufacture. In accordance with the illustrativeembodiment, the fiducial reference point can be:

-   -   (i) on the surface of the material composing the article of        manufacture, or    -   (ii) within (i.e., buried) the material composing the article of        manufacture (when using a frustum of a pyramidal melting tip),        or    -   (iii) outside the material composing the article of manufacture        with no tangible connection to the article of manufacture.

When pyramidal melting tip 255 is used to establish a fiducial referencepoint, the fiducial reference point is represented by the apex of apyramid. It is well known to those skilled in the art that the apex of apyramid—like a fiducial reference point—is a geometric point.

In accordance with the illustrative embodiment, pyramidal melting tip255 establishes a fiducial reference point (i.e., the apex of a pyramid)at a location in the coordinate system of the article of manufacture bymelting a hole into the material that composes the article ofmanufacture, wherein the hole is defined, at least in part, by a portionof a tangible pyramidal surface.

Thereafter, the location of the apex of the pyramid (i.e., the fiducialreference point) can be determined by probing a portion of the tangiblepyramidal surface to determine the spatial parameters of the pyramid.After the spatial parameters of the pyramid are determined, it is wellknown to those skilled in the art how to determine the apex of thepyramid (i.e., the fiducial reference point). A probe that isspecifically designed for probing the portion of the tangible pyramidalsurface and determining its spatial parameters is described below and inthe accompanying figures.

Referring again to FIGS. 7a, 7b, and 7c , pyramidal melting tip 255comprises a shank, a body, and a melting surface.

In accordance with the illustrative embodiment, pyramidal melting tip255 is fabricated out of steel, but it will be clear to those skilled inthe art how to make and use alternative embodiments of the presentinvention in which a pyramidal drill bit is fabricated out of anothermaterial or materials.

In accordance with the illustrative embodiment, the shank of pyramidalmelting tip 255 has a length of 2 cm and a diameter of 1 cm It will beclear to those skilled in the art how to make and use alternativeembodiments of the present invention in which the shank has differentdimensions.

In accordance with the illustrative embodiment, the body of pyramidalmelting tip 255 has a length of 3 cm and a diameter of 3 cm. It will beclear to those skilled in the art how to make and use alternativeembodiments of the present invention in which the body has differentdimensions.

In accordance with the illustrative embodiment, the melting surface ofpyramidal melting tip 255 comprises the three faces of a regulartriangular pyramid. The apex of the pyramid is collinear with the axisof the shank and body of pyramidal melting tip 255. In addition, thedihedral angle between each pair of faces equals cos⁻¹(⅓)≈70.52°. Itwill be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which the melting surface of a pyramidal melting tipcomprises any pyramid (e.g., an irregular three-sided pyramid, a regularfour-sided pyramid, an irregular four-sided pyramid, a regularfive-sided pyramid, etc.).

It will also be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which the melting surface of a pyramidal melting tipcomprises only the frustum of a pyramid. When, for example, afrustum-of-a-pyramid melting tip is used to melt a blind hole into thematerial composing an article of manufacture, the apex of the pyramidcan be buried within the material or, alternatively, outside thematerial on the inferior side of the material.

Pyramidal melting tip 255 is capable of melting a “blind” hole into thematerial (e.g., thermoplastic, fiber-reinforced thermoplastic,thermoset, fiber-reinforced thermoset, metal, glass, ceramic, composite,etc.) composing the article of manufacture such that the blind hole isdefined, at least in part, by a portion of a tangible pyramidal surface.FIGS. 22a, 22b, and 22c depict a blind hole—pyramidal blind hole2200—that is defined by a portion of a tangible pyramidal surface.

Pyramidal melting tip 255 is also capable of melting a “through” holeinto the material (e.g., thermoplastic, fiber-reinforced thermoplastic,thermoset, fiber-reinforced thermoset, metal, glass, ceramic, composite,etc.) composing the article of manufacture such that the through hole isdefined, at least in part, by a portion of a tangible pyramidal surface.FIGS. 23a, 23b, and 23c depict a through hole—pyramidal through hole2300—that is defined by a portion of a tangible pyramidal surface.

In accordance with the illustrative embodiment, each pyramidal blindhole and each pyramidal through hole is characterized by two metrics:

(i) the “pyramidal-surface area,” and

(ii) the “pyramidal-surface volume.”

The pyramidal-surface area and the pyramidal-surface volume can be, butare not necessarily, related to:

(i) the amount of material removed to create the hole, or

(ii) the contour of the superior surface before or after the hole iscreated, or

(iii) the contour of the inferior surface (if any) before or after thehole is created.

For the purposes of this specification, the term “pyramidal-surfacearea” is defined as the area of the portion of the tangible pyramidalsurface in the hole. For example, when the superior surface is planarand the pyramidal axis is normal to the superior surface, thepyramidal-surface area S of a pyramidal blind hole equals:S=√{square root over (3)}a ²  (Eq. 9)where a is the base edge length of one pyramidal face at the planecontaining the superior surface. As another example, when the superiorand inferior surfaces are planar and parallel and the pyramidal axis isnormal to the superior surface, the pyramidal-surface area S of apyramidal through hole equals:S=√{square root over (3)}(a ² −b ²)  (Eq. 10)where a is the base edge length of one pyramidal face at the planecontaining the superior surface, and where b is the base edge length ofone pyramidal face at the plane containing the inferior surface. It willbe clear to those skilled in the art how to calculate (analytically ornumerically) and measure empirically the pyramidal-surface area of anypyramidal blind hole and any pyramidal through hole.

For the purposes of this specification, the term “pyramidal-surfacevolume” is defined as the volume of three-dimensional space that issurrounded by the portion of the tangible pyramidal surface in the hole.For example, when the superior surface is planar, the pyramid is aregular triangular pyramid, and the axis of the pyramid is normal to thesuperior surface, the pyramidal-surface volume V of a pyramidal blindhole equals:

$\begin{matrix}{V = \frac{a^{3}}{6\sqrt{2}}} & \left( {{Eq}.\mspace{14mu} 11} \right)\end{matrix}$where a is the distance from the apex to the superior surface along thelateral edge of a face of the pyramid. As another example, when thesuperior and inferior surfaces are planar and parallel, the pyramid is aregular triangular pyramid, and the axis of the pyramid is normal to thesuperior surface, the pyramidal-surface volume V of a pyramidal throughhole equals:

$\begin{matrix}{V = \frac{a^{3} - b^{3}}{6\sqrt{2}}} & \left( {{Eq}.\mspace{14mu} 12} \right)\end{matrix}$where a is the distance from the apex to the superior surface along thelateral edge of a face of the pyramid and b is the distance from theapex to the inferior surface along the lateral edge of a face of thepyramid. It will be clear to those skilled in the art how to calculate(analytically or numerically) and measure empirically the volume of anypyramidal blind hole and any pyramidal through hole regardless of thecontour of the superior and inferior surfaces, regardless of therelationship of the superior and inferior surfaces, and regardless ofthe relationship of the pyramidal axis to the superior surface.

In accordance with the illustrative embodiment it is expected thatvariations in manufacturing will cause variations in the mass, volume,and dimensions of fabricated articles of manufacture that, in turn, willlead to:

-   -   (i) variations in the pyramidal-surface volumes of the pyramidal        holes (blind and through) in a single article of manufacture,        and    -   (ii) variations in the pyramidal-surface volumes of        corresponding pyramidal holes (blind and through) in        corresponding articles of manufacture, and    -   (iii) variations in the pyramidal-surface areas of the pyramidal        holes (blind and through) in a single article of manufacture,        and    -   (ii) variations in the pyramidal-surface areas of corresponding        pyramidal holes (blind and through) in corresponding articles of        manufacture.

In accordance with the illustrative embodiment, the material composingan article of manufacture comprises:

(i) one, two, three, four, or more pyramidal blind holes, or

(ii) one, two, three, four, or more pyramidal through holes, or

(iii) any combination of i and ii.

It will be clear to those skilled in the art, after reading thisdisclosure, how to make and use pyramidal melting tip 255.

FIGS. 8a, 8b, and 8c depict the orthogonal front, side, and bottomviews, respectively, of conic probe 256 in accordance with theillustrative embodiment of the present invention. Conic probe 256 isused by the illustrative embodiment to locate the conical apex (i.e.,the fiducial reference point) that is associated with a hole in thematerial composing an article of manufacture, which hole is defined, atleast in part, by a portion of a tangible conical surface (e.g., a holemade by conic drill bit 251, a hole made by conic melting tip 253, etc).In accordance with the illustrative embodiment, the mating surface ofconic probe 256 is the complement of part of the conic cutting surfaceon conic drill bit 251 and the conic melting surface on conic meltingtip 253, and, therefore, the mating surface fits into the tangibleconical surface when the axis of the probe is collinear with the axis ofthe portion of the tangible conical surface. When the mating surface ofconic probe 256 fits into the portion of the tangible conical surface,then the spatial parameters of the tangible conical surface can beeasily determined. Conic probe 256 works with both blind holes and withthrough holes.

Referring to FIGS. 8a, 8b, and 8c , conic probe 256 comprises a shank, abody, and a mating surface.

In accordance with the illustrative embodiment, conic probe 256 isfabricated out of steel, but it will be clear to those skilled in theart how to make and use alternative embodiments of the present inventionin which a conic probe is fabricated out of one or more other materials.

In accordance with the illustrative embodiment, the shank of conic probe256 has a length of 2 cm and a diameter of 1 cm. It will be clear tothose skilled in the art, after reading this disclosure, how to make anduse alternative embodiments of the present invention in which the shankhas different dimensions.

In accordance with the illustrative embodiment, the body of conic probe256 has a length of 4 cm and a diameter of 3 cm. It will be clear tothose skilled in the art, after reading this disclosure, how to make anduse alternative embodiments of the present invention in which the bodyhas different dimensions.

In accordance with the illustrative embodiment, the mating surface ofconic probe 256 is the frustum of a 1 cm high right circular cone whoseapex angle corresponds to the apex angle of conic drill bit 251 andconic melting tip 253. The frustum of the cone is bounded by the lowerfrustum base and the upper frustum base. The mating surface of conicprobe 256 is the frustum of a cone rather than a cone so that smallamounts of dirt and debris that accumulate in the hole do not hamper thefitting of conic probe 256 into the hole. It will, however, be clear tothose skilled in the art, after reading this disclosure, how to make anduse alternative embodiments of the present invention in which the conicprobe is a full cone.

It will be clear to those skilled in the art, after reading thisdisclosure, how to make and use conic probe 256.

FIGS. 9a, 9b, and 9c depict the orthogonal front, side, and bottomviews, respectively, of spheroidal probe 257 in accordance with theillustrative embodiment of the present invention. Spheroidal probe 257is used by the illustrative embodiment to locate the center of aspheroid (i.e., the fiducial reference point) that is associated with ahole in the material composing an article of manufacture, which hole isdefined at least in part, by a portion of a tangible spheroidal surface.In accordance with the illustrative embodiment, the mating surface ofspheroidal probe 257 has the same radius as the cutting surface onspheroidal drill bit 252 and the spheroidal melting surface on meltingtip 254. When the mating surface of spheroidal probe 257 fits into theportion of the melting surface, then the center of the spheroid (i.e.,the fiducial reference point) can be easily determined. Spheroidal probe257 works with both blind holes and with through holes.

Referring to FIGS. 9a, 9b, and 9c , spheroidal probe 257 comprises ashank, a body, and a mating surface.

In accordance with the illustrative embodiment, spheroidal probe 257 isfabricated out of steel, but it will be clear to those skilled in theart how to make and use alternative embodiments of the present inventionin which a spheroidal probe is fabricated out of one or more othermaterials.

In accordance with the illustrative embodiment, the shank of spheroidalprobe 257 has a length of 2 cm and a diameter of 1 cm. It will be clearto those skilled in the art, after reading this disclosure, how to makeand use alternative embodiments of the present invention in which theshank has different dimensions.

In accordance with the illustrative embodiment, the body of spheroidalprobe 257 has a length of 4 cm and a diameter of 3 cm. It will be clearto those skilled in the art, after reading this disclosure, how to makeand use alternative embodiments of the present invention in which thebody has different dimensions.

In accordance with the illustrative embodiment, the mating surface ofspheroidal probe 257 is a 1 cm high frustum of a hemisphere whose radiuscorresponds to the radius of spheroidal drill bit 252 and spheroidalmelting tip 254. The frustum of the hemisphere is bounded by the lowerfrustum base and the upper frustum base. The mating surface ofspheroidal probe 257 is the frustum of a hemisphere rather than ahemisphere so that small amounts of dirt and debris that accumulate inthe hole do not hamper the fitting of spheroidal probe 257. It will,however, be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which the spheroidal probe has the shape of a spheroidalcap.

It will be clear to those skilled in the art, after reading thisdisclosure, how to make and use spheroidal probe 257.

FIGS. 10a, 10b, and 10c depict the orthogonal front, side, and bottomviews, respectively, of pyramidal probe 258 in accordance with theillustrative embodiment of the present invention. Pyramidal probe 258 isused by the illustrative embodiment to locate the apex of a pyramid(i.e., the fiducial reference point) that is associated with a hole inthe material composing an article of manufacture, which hole is defined,at least in part, by a portion of three pyramidal faces (e.g., a holemade by pyramidal melting tip 255, etc.). In accordance with theillustrative embodiment, the mating surface of pyramidal probe 258 isthe complement of the pyramidal melting surface on pyramidal melting tip255 (i.e., the three faces of a regular triangular pyramid). When themating surface of pyramidal probe 258 fits into the portions of thethree faces, the spatial parameters of the plane containing each facecan be determined. After the spatial parameters of each plane aredetermined, the location of the apex of the pyramid (i.e., the fiducialreference point) can be determined (because it is where the planesintersect). Pyramidal probe 258 works with both blind holes and withthrough holes.

In accordance with the illustrative embodiment, pyramidal probe 258comprises a shank, a body, and a mating surface.

Pyramidal probe 258 is fabricated out of steel, but it will be clear tothose skilled in the art how to make and use alternative embodiments ofthe present invention in which a pyramids probe is fabricated out of oneor more other materials.

In accordance with the illustrative embodiment, the shank of pyramidalprobe 258 has a length of 2 cm and a diameter of 1 cm. It will be clearto those skilled in the art, after reading this disclosure, how to makeand use alternative embodiments of the present invention in which theshank has different dimensions.

In accordance with the illustrative embodiment, the body of pyramidalprobe 258 has a length of 3 cm and a diameter of 3 cm. It will be clearto those skilled in the art, after reading this disclosure, how to makeand use alternative embodiments of the present invention in which thebody has different dimensions.

In accordance with the illustrative embodiment, the mating surface ofpyramidal probe 258 is a 1.5 cm high frustum of a regular triangularpyramid (i.e., a tetrahedron) whose faces and angles correspond to thefaces and angles of pyramidal melting tip 255. The frustum of thepyramid is bounded by the lower frustum base and the upper frustum base.The mating surface of pyramidal probe 258 is the frustum of a pyramidrather than a full pyramid so that small amounts of dirt and debris thataccumulate in the hole do not hamper the fitting of pyramidal probe 258.

FIG. 11 depicts a flowchart of the operation of the illustrativeembodiment of the present invention.

At task 1101, a natural person, in conjunction with a computer-aideddesign system, designs:

-   -   (i) an article of manufacture to be fabricated by additive        manufacturing system 100, and    -   (ii) the set of fiducial reference points to be embodied into        the article, after it is fabricated, by registration system 200.        In accordance with the illustrative embodiment, there are no        constraints on the size, shape, contour, or materials of the        article of manufacture. The article can be complex or relatively        simple.

For example, FIGS. 12a, 12b, and 12c depict the orthogonal front, side,and top views of the design for a first illustrative article ofmanufacture—solid hemisphere 1200, which is to be made of a carbon-fiberreinforced thermoplastic that has a density of 1.3 grams/cm³. Solidhemisphere 1200 is specified to have a radius of 100 cm, a volume of≈20,944 cm³, and a mass of ≈27,227 grams (before the representativefiducial marks are embedded). The coordinate system for solid hemisphere1200 has its origin at the center of the sphere from which solidhemisphere 1200 is formed.

As another example, FIGS. 13a, 13b, and 13c depict the orthogonal front,side, and top views of the design for a second illustrative article ofmanufacture—hemispherical shell 1300, which is to be made of acarbon-fiber reinforced thermoplastic that has a density of 1.3grams/cm³. Hemispherical shell 1300 is specified to have an outer radiusof 100 cm and an inner radius of 99 cm (i.e., the thickness of the shellis 1 cm), a volume of ≈417 cm³, and a mass of ≈542 grams (before therepresentative fiducial marks are embedded). The coordinate system forhemispherical shell 1300 has its origin at the center of the sphere fromwhich hemispherical shell 1300 is formed.

As part of task 1101, the natural person, in conjunction with thecomputer-aided design system, decides how many fiducial reference pointsare to be associated with the article of manufacture. It is well knownto those skilled in the art that a “rigid body” requires threenon-collinear fiducial reference points to establish (1) linearposition, and (2) angular position (which is also known as ‘orientation’or ‘attitude’). It is well known to those skilled in the art, that thereare situations and conditions and contests when it is necessary oradvantageous to associated more that three (e.g., four, five, six,eight, ten, etc.) fiducial reference points with an article ofmanufacture.

In accordance with the first illustrative article of manufacture, solidhemisphere 1200 is to be associated with four (4) fiducial referencepoints.

In accordance with the second illustrative article of manufacture,hemispherical shell 1300 is to be associated with four (4) fiducialreference points.

It will be clear to those skilled in the art, after reading thisdisclosure, how to decide how many fiducial reference points are to beassociated with any article of manufacture.

As part of task 1101, the natural person, in conjunction with thecomputer-aided design system, decides where the fiducial referencepoints should be with regard to article of manufacture. It is well knownto those skilled in the art that, in general, three fiducial referencepoints should not be collinear and that, in general, four fiducialreference points should not be coplanar. Furthermore, it is generallyadvantageous to have greater distances between fiducial reference pointsbecause it facilitates greater accuracy in lateral and angular position.

In accordance with the first illustrative article of manufacture, thecoordinates of the four fiducial reference points associated with solidhemisphere 1200 are presented in Table 1.

TABLE 1 Coordinates of the Fiducial Reference Points in Solid Hemisphere1200 Fiducial Reference Point Coordinates Distance from Origin 1201-1 (0cm, 69.6 cm, 69.6 cm) 98.4 cm 1201-2 (70 cm, 0 cm, 70 cm) 99.0 cm 1201-3(0 cm, −69.6 cm, 69.6 cm) 98.4 cm 1201-4 (−70 cm, 0 cm, 70 cm) 99.0 cm

From Table 1, it can be seen that no three fiducial reference points arecollinear, the four fiducial reference points are non-coplanar, and allfour fiducial reference points are within solid hemisphere 1200.

In accordance with the second illustrative article of manufacture, thecoordinates of the four fiducial reference points associated withhemispherical shell 1300 are presented in Table 2.

TABLE 2 Coordinates of the Fiducial Reference Points in HemisphericalShell 1300 Fiducial Reference Point Coordinates Distance from Origin1301-1 (0 cm, 69.6 cm, 69.6 cm) 98.4 cm 1301-2 (70.3 cm, 0 cm, 70.3 cm)99.4 cm 1301-3 (0 cm, −69.6 cm, 69.6 cm) 98.4 cm 1301-4 (−70.3 cm, 0 cm,70.3 cm) 99.4 cm

From Table 2, it can be seen that no three fiducial reference points arecollinear, the four fiducial reference points are non-coplanar.Furthermore, two fiducial reference points—1301-1 and 1301-3 are notwithin hemispherical shell 1300 (i.e., will be memorialized with conicalthrough holes), and two fiducial reference points—1301-2 and 1301-4 arewithin hemispherical shell 1300 (i.e., will be memorialized with conicalblind holes).

It will be clear to those skilled in the art, after reading thisdisclosure, how to decide where the fiducial reference points should be.

As part of task 1101, the natural person, in conjunction with thecomputer-aided design system, decides what kind of representativefiducial mark is to be incorporated into the article of manufacture tomemorialize each fiducial reference point.

In accordance with the first illustrative article of manufacture, thefour fiducial reference points are to be memorialized by conical blindholes created with conic drill bit 251. For each hole, the approachangle of the hole is normal to the surface of solid hemisphere 1200 (asshown by the arrows in FIGS. 12a, 12b, and 12c ).

A conic fiducial mark comprises a conical axis. In accordance with theillustrative embodiment, the conic axes associated with the fiducialreference points 1201-1 and 1201-3, respectively, are planar andintersect (i.e., the two axes are non-parallel and not skew), and theconic axes associated with the fiducial reference points 1201-2 and1201-4, respectively, are planar and intersect (i.e., the two axes arenon-parallel and not skew). Furthermore, the conic axes associated withthe fiducial reference points 1201-1 and 1201-2, respectively, are skew,and the conic axes associated with the fiducial reference points 1201-3and 1201-4, respectively, are skew.

In accordance with the second illustrative article of manufacture, thefiducial reference points 1301-1, 1301-2, 1301-3, and 1301-4 are to bememorialized by spheroidal blind holes created with spheroidal drill bit252. For each hole, the approach angle of the hole is normal to thesurface of hemispherical shell 1300 (as shown by the arrows in FIGS.13a, 13b, and 13c ).

It will be clear to those skilled in the art, after reading thisdisclosure, how to make and use alternative embodiments of the presentinvention in which each of the fiducial reference points is memorializedby a different kind of representative fiducial mark, and any combinationof representative fiducial marks. For example, an article of manufacturecan comprise:

(i) one, two, three, or four conical blind holes, or

(ii) one, two, three, or four conical through holes, or

(iii) one, two, three, or four spheroidal blind holes, or

(iv) one, two, three, or four spheroidal through holes, or

(v) one, two, three, or four pyramidal blind holes, or

(vi) one, two, three, or four pyramidal through holes, or

(vii) any combination of i, ii, iii, iv, v, and vi.

Conical fiducial marks and (non-spherical) spheroidal fiducial markscomprise an axis of symmetry and pyramidal fiducial marks comprise apyramidal axis. It will be clear to those skilled in the art, afterreading this disclosure, how to make and use alternative embodiments ofthe present invention in which each pair of axes is collinear,non-collinear, parallel, not parallel, planar, non-planar, or skew. Forexample, an article of manufacture can comprise:

(i) two, three, or four representative fiducial marks whose axes arecollinear, or

(ii) two, three, or four representative fiducial marks whose axes arenon-collinear, or

(iii) two, three, or four representative fiducial marks whose axes areparallel, or

(iv) two, three, or four representative fiducial marks whose axes arenon-parallel, or

(v) two, three, or four representative fiducial marks whose axes areplanar, or

(vi) two, three, or four representative fiducial marks whose axes arenon-planar, or

(vii) two, three, or four representative fiducial marks whose axes areskew, or

(viii) two, three, or four representative fiducial marks whose axes arenot skew, or

(ix) any combination of i, ii, iii, iv, v, vi, vii, and viii.

It will be clear to those skilled in the art, however, after readingthis disclosure, how to make and use alternative embodiments of solidhemisphere 1200—or any article of manufacture—that use any non-empty setof representative fiducial marks.

It will be clear to those skilled in the art, after reading thisdisclosure, how to accomplish task 1101.

At task 1102, a first article of manufacture and a second article ofmanufacture are fabricated by additive manufacturing system 100, inwell-known fashion.

FIGS. 14a, 14b, and 14c depict the orthogonal front, side, and topviews, respectively, of solid hemisphere 1400 as it was actuallyfabricated. Whereas solid hemisphere 1400 was designed to have a uniformradius of 100 cm, it was, in fact, fabricated with non-trivialdimensional variations. For example, the outer radius through fiducialreference mark 1201-1 is 100.2 cm, the outer radius through fiducialreference mark 1201-2 is 99.8 cm, the outer radius through fiducialreference mark 1201-3 is 99.9 cm, and the outer radius through fiducialreference mark 1201-4 is 100.5 cm. This summarized in Table 3.

TABLE 3 Outer Radius, as Fabricated, of Solid Hemisphere 1400 FiducialOuter Radius Conical-Surface Conical-Surface Reference Point asFabricated Volume of Hole Area of Hole 1201-1 100.2 cm ≈2.04 cm³  ≈10.18cm² 1201-2  99.8 cm ≈0.18 cm³ ≈2.01 cm² 1201-3  99.9 cm ≈1.18 cm³ ≈7.07cm² 1201-4 100.5 cm ≈1.18 cm³ ≈7.07 cm²

Furthermore, the actual volume of solid hemisphere 1400 as fabricated is≈20,877 cm³ and the actual mass is ≈27,140 gr (before the representativefiducial marks are embedded).

FIGS. 15a, 15b, and 15c depict the orthogonal front, side, and topviews, respectively, of solid hemisphere 1500 as it was actuallyfabricated. Whereas solid hemisphere 1500 was designed to have a uniformradius of 100 cm, it was, in fact, fabricated with non-trivialdimensional variations. For example, the outer radius through fiducialreference mark 1201-1 is 100.4 cm, the outer radius through fiducialreference mark 1201-2 is 99.6 cm, the outer radius through fiducialreference mark 1201-3 is 100.3 cm, and the outer radius through fiducialreference mark 1201-4 is 99.9 cm. This summarized in Table 4.

TABLE 4 Outer Radius, as Fabricated, of Solid Hemisphere 1500 FiducialOuter Radius Conical-Surface Conical-Surface Reference Point asFabricated Volume of Hole Area of Hole 1201-1 100.4 cm ≈2.79 cm³  ≈12.57cm² 1201-2  99.6 cm ≈0.08 cm³ ≈1.13 cm² 1201-3 100.3 cm ≈2.39 cm³ ≈11.34 cm² 1201-4  99.9 cm ≈0.25 cm³ ≈2.54 cm²

Furthermore, the actual volume of solid hemisphere 1500 as fabricated is≈20,756 cm³ and the actual mass is ≈26,983 gr (before the representativefiducial marks are embedded).

FIGS. 16a, 16b, and 16c depict the orthogonal front, side, and topviews, respectively, of hemispherical shell 1600 as it was actuallyfabricated. Whereas hemispherical shell 1600 was designed to have auniform outer radius of 100 cm and a uniform inner radius of 99 cm, theouter radius was, in fact, fabricated with non-trivial dimensionalvariations. The inner radius was fabricated exactly as designed at 99cm. For example, the outer radius through fiducial reference mark 1301-1is 99.6 cm, the outer radius through fiducial reference mark 1301-2 is100.0 cm, the outer radius through fiducial reference mark 1301-3 is100.3 cm, and the outer radius through fiducial reference mark 1301-4 is100.4 cm. This summarized in Table 5.

TABLE 5 Outer Radius, as Fabricated, of Hemispherical Shell 1600Fiducial Outer Radius Conical-Surface Conical-Surface Reference Point asFabricated Volume of Hole Area of Hole 1301-1  99.6 cm ≈0.53 cm³ ≈3.39cm² 1301-2 100.0 cm ≈0.08 cm³ ≈1.13 cm² 1301-3 100.3 cm ≈2.32 cm³ ≈10.21 cm² 1301-4 100.4 cm ≈0.35 cm³ ≈3.14 cm²

Furthermore, the actual volume of hemispherical shell 1600 as fabricatedis ≈425 cm³ and the actual mass is ≈553 gr (before the representativefiducial marks are embedded).

FIGS. 17a, 17b, and 17c depict the orthogonal front, side, and topviews, respectively, of hemispherical shell 1700 as it was actuallyfabricated. Whereas hemispherical shell 1700 was designed to have auniform outer radius of 100 cm and a uniform inner radius of 99 cm, theouter radius was, in fact, fabricated with non-trivial dimensionalvariations. The inner radius was fabricated exactly as designed at 99cm. For example, the outer radius through fiducial reference mark 1301-1is 100.2 cm, the outer radius through fiducial reference mark 1301-2 is100.6 cm, the outer radius through fiducial reference mark 1301-3 is99.9 cm, and the outer radius through fiducial reference mark 1301-4 is99.8 cm. This summarized in Table 6.

TABLE 6 Outer Radius, as Fabricated, of Hemispherical Shell 1700Fiducial Outer Radius Conical-Surface Conical-Surface Reference Point asFabricated Volume of Hole Area of Hole 1301-1 100.2 cm ≈1.96 cm³ ≈9.05cm² 1301-2 100.6 cm ≈0.60 cm³ ≈4.52 cm² 1301-3  99.9 cm ≈1.10 cm³ ≈5.94cm² 1301-4  99.8 cm ≈0.02 cm³ ≈0.50 cm²

Furthermore, the actual volume of hemispherical shell 1700 as fabricatedis ≈421 cm³ and the actual mass is ≈547 gr (before the representativefiducial marks are embedded).

It will be clear to those skilled in the art, after reading thisdisclosure, how to accomplish task 1102.

At task 1103, registration system 100 imparts the representativefiducial marks into the first article of manufacture and into the secondfabricated art, as specified in task 1101. Task 1103 is described indetail below and in the accompanying figures. It will be clear to thoseskilled in the art, after reading this disclosure, how to accomplishtask 1103.

At task 1104, registration system 100 locates the first article ofmanufacture and the second article of manufacture based on theirrepresentative fiducial marks. Task 1104 is described in detail belowand in the accompanying figures. It will be clear to those skilled inthe art, after reading this disclosure, how to accomplish task 1104.

At task 1105, the first article of manufacture and the second article ofmanufacture are subject to secondary processing that is possible becausetheir respective lateral and angular locations were determined in task1104.

The location of solid hemisphere 1400 and the location of solidhemisphere 1500 are used to position them, respectively, so that theycan be glued—in well-known fashion—into a solid sphere. In particular,solid hemisphere 1400 and solid hemisphere 1500 are positioned so thattheir origins coincide. Afterwards, the solid sphere is sanded andpainted in well-known fashion.

The location of hemispherical shell 1600 and the location ofhemispherical shell 1700 are used to position them, respectively, sothat they can be glued—in well-known fashion—into a spherical shell. Inparticular, hemispherical shell 1600 and hemispherical shell 1700 arepositioned so that their origins coincide. Afterwards, the sphericalshell is sanded and painted in well-known fashion.

It will be clear to those skilled in the art, after reading thisdisclosure, how to accomplish task 1104.

FIG. 24 depicts a flowchart of the salient tasks associated with theperformance of task 1103—embodying the representative fiducial marksinto the fabricated articles of manufacture.

At task 2401, registration system 200 establishes the first fiducialreference point with the article of manufacture by removing a firstportion of the material composing the article of manufacture to create afirst hole, wherein the first hole is defined, at least in part, by aportion of the surface of a representative fiducial mark.

Registration system 200 establishes fiducial reference point 1201-1 withsolid hemisphere 1400 by using conical drill bit 251 to drill a conicalblind hole 1.8 cm into the superior surface with a conical axis that isnormal to the superior surface. The volume and tangible conical-surfacearea of the resulting tangible conical surface is given in Table 3.

Registration system 200 establishes fiducial reference point 1201-1 withsolid hemisphere 1500 by using conical drill bit 251 to drill a conicalblind hole 2.0 cm into the superior surface with a conical axis that isnormal to the superior surface. The volume and tangible conical-surfacearea of the resulting tangible conical surface is given in Table 4.

Registration system 200 establishes fiducial reference point 1301-1 withhemispherical shell 1600 by using conical drill bit 251 to drill aconical through hole 1.2 cm into the superior surface with a conicalaxis that is normal to the superior surface. The volume and tangibleconical-surface area of the resulting tangible conical surface is givenin Table 5.

Registration system 200 establishes fiducial reference point 1301-1 withhemispherical shell 1700 by using conical drill bit 251 to drill aconical through hole 1.8 cm into the superior surface with a conicalaxis that is normal to the superior surface. The volume and tangibleconical-surface area of the resulting tangible conical surface is givenin Table 6.

At task 2402, registration system 200 establishes the second fiducialreference point with the article of manufacture by removing a secondportion of the material composing the article of manufacture to create asecond hole, wherein the second hole is defined, at least in part, by aportion of the surface of a representative fiducial mark.

Registration system 200 establishes fiducial reference point 1201-2 withsolid hemisphere 1400 by using conical drill bit 251 to drill a conicalblind hole 0.8 cm into the superior surface with a conical axis that isnormal to the superior surface. The volume and tangible conical-surfacearea of the resulting tangible conical surface is given in Table 3.

Registration system 200 establishes fiducial reference point 1201-2 withsolid hemisphere 1500 by using conical drill bit 251 to drill a conicalblind hole 0.6 cm into the superior surface with a conical axis that isnormal to the superior surface. The volume and tangible conical-surfacearea of the resulting tangible conical surface is given in Table 4.

Registration system 200 establishes fiducial reference point 1301-2 withhemispherical shell 1600 by using conical drill bit 251 to drill aconical blind hole 0.6 cm into the superior surface with a conical axisthat is normal to the superior surface. The volume and tangibleconical-surface area of the resulting tangible conical surface is givenin Table 5.

Registration system 200 establishes fiducial reference point 1301-2 withhemispherical shell 1700 by using conical drill bit 251 to drill aconical blind hole 1.2 cm into the superior surface with a conical axisthat is normal to the superior surface. The volume and tangibleconical-surface area of the resulting tangible conical surface is givenin Table 6.

At task 2403, registration system 200 establishes the third fiducialreference point with the article of manufacture by removing a thirdportion of the material composing the article of manufacture to create athird hole, wherein the third hole is defined, at least in part, by aportion of the surface of a representative fiducial mark.

Registration system 200 establishes fiducial reference point 1201-3 withsolid hemisphere 1400 by using conical drill bit 251 to drill a conicalblind hole 1.5 cm into the superior surface with a conical axis that isnormal to the superior surface. The volume and tangible conical-surfacearea of the resulting tangible conical surface is given in Table 3.

Registration system 200 establishes fiducial reference point 1201-3 withsolid hemisphere 1500 by using conical drill bit 251 to drill a conicalblind hole 1.9 cm into the superior surface with a conical axis that isnormal to the superior surface. The volume and tangible conical-surfacearea of the resulting tangible conical surface is given in Table 4.

Registration system 200 establishes fiducial reference point 1301-3 withhemispherical shell 1600 by using conical drill bit 251 to drill aconical through hole 1.9 cm into the superior surface with a conicalaxis that is normal to the superior surface. The volume and tangibleconical-surface area of the resulting tangible conical surface is givenin Table 5.

Registration system 200 establishes fiducial reference point 1301-3 withhemispherical shell 1700 by using conical drill bit 251 to drill aconical through hole 1.5 cm into the superior surface with a conicalaxis that is normal to the superior surface. The volume and tangibleconical-surface area of the resulting tangible conical surface is givenin Table 6.

At task 2404, registration system 200 establishes the fourth fiducialreference point with the article of manufacture by removing a fourthportion of the material composing the article of manufacture to create afourth hole, wherein the fourth hole is defined, at least in part, by aportion of the surface of a representative fiducial mark.

Registration system 200 establishes fiducial reference point 1201-4 withsolid hemisphere 1400 by using conical drill bit 251 to drill a conicalblind hole 1.5 cm into the superior surface with a conical axis that isnormal to the superior surface. The volume and tangible conical-surfacearea of the resulting tangible conical surface is given in Table 3.

Registration system 200 establishes fiducial reference point 1201-4 withsolid hemisphere 1500 by using conical drill bit 251 to drill a conicalblind hole 0.9 cm into the superior surface with a conical axis that isnormal to the superior surface. The volume and tangible conical-surfacearea of the resulting tangible conical surface is given in Table 4.

Registration system 200 establishes fiducial reference point 1301-4 withhemispherical shell 1600 by using conical drill bit 251 to drill aconical blind hole 1.0 cm into the superior surface with a conical axisthat is normal to the superior surface. The volume and tangibleconical-surface area of the resulting tangible conical surface is givenin Table 5.

Registration system 200 establishes fiducial reference point 1301-4 withhemispherical shell 1700 by using conical drill bit 251 to drill aconical blind hole 0.4 cm into the superior surface with a conical axisthat is normal to the superior surface. The volume and tangibleconical-surface area of the resulting tangible conical surface is givenin Table 6.

At the end of task 1103 (after material has been removed as part of theprocess of embedding the representative fiducial marks) solid hemisphere1400 and solid hemisphere 1500 have similar (but different) volumes,similar (but different) masses, and similar (but different) shapes.Regardless of their differences, the relative location of the fiducialreference points is identical. In fact, each triplet of correspondingfiducial reference points is a congruent triangle—regardless of the factthat the two articles have different volumes, masses, and shapes.

The volume, mass, and shape similarity of solid hemisphere 1400 andsolid hemisphere 1500 are presented in Table 7.

TABLE 7 Volume, Mass, and Shape Similarity of Solid Hemisphere 1400 andSolid Hemisphere 1500 Unilateral Bilateral Article of Shape ShapeManufacture Volume Mass Similarity Similarity Solid ≈20,873 cm³ ≈27,134gr ≈0.985 ≈0.989 Hemisphere 1400 Solid ≈20,750 cm³ ≈26,975 gr ≈0.993Hemisphere 1500

For the purposes of this specification, the similarity of the volume ofspace occupied by two articles of manufacture is characterized by twometrics:

(i) the “unilateral shape similarity,” and

(ii) the “bilateral shape similarity.”

The unilateral shape similarity of volume a with respect to volume b(notated as a # b) equals the maximum percentage of volume a that can besuperimposed, without deformation, within volume b. In some cases, thereis only one superposition of volume a and volume b that yields themaximum percentage. In other cases, there are two or more superpositionsof volume a and volume b that yield the maximum percentage.

The bilateral shape similarity of volume a with respect to volume b(notated as a Δ b) equals the harmonic mean of:

(i) the unilateral shape similarity of volume a with respect to volumeb, (a # b), and

(ii) the unilateral shape similarity of volume b with respect to volumea, (b # a).

Mathematically, the bilateral shape similarity of a Δ b equals:

$\begin{matrix}{{a\;\Delta\; b} = \frac{2}{\frac{1}{a\# b} + \frac{1}{b\# a}}} & \left( {{Eq}.\mspace{14mu} 13} \right)\end{matrix}$

For example, a sphere with a radius of 1 cm can be wholly superimposed,without deformation, within a sphere with a radius of 2 cm, and,therefore, the unilateral shape similarity of the smaller sphere withrespect to the larger sphere is 100% or 1. In contrast, only a portionof the larger sphere can be superimposed, without deformation, withinthe smaller sphere, and, therefore, the unilateral shape similarity ofthe larger sphere with respect to the smaller sphere is 12.5% or 0.125.The bilateral shape similarity of the two spheres is ≈0.2222.

As another example, consider a first block that is 5 cm×2 cm×2 cm and asecond block that is 4 cm×3 cm×2 cm. Only a portion of the first blockcan be superimposed, without deformation, within the second block, andthe unilateral shape similarity of the first block with respect to thesecond block is 80% or 0.80. Only a portion of the second block can besuperimposed, without deformation, within the first block, and theunilateral shape similarity of the second block with respect to thefirst block is 66⅔% or ≈0.6666. The bilateral shape similarity of thetwo blocks is ≈0.7272.

The unilateral shape similarity operation is not commutative:a#b≠b#a  (Eq. 14)

By definition, the unilateral shape similarity of a # a=1 (because thevolume of an object fits perfectly within itself), and the unilateralshape similarity of a # b>0 (because one point in object a can always besuperimposed with at least one point in object b). Therefore, the rangeof values of unilateral shape similarity is:0<a#b≤1  (Eq. 15)It will be clear to those skilled in the art, after reading thisdisclosure, how to calculate (analytically or numerically) or determineempirically, the unilateral shape similarity of any two articles ofmanufacture. In accordance with the illustrative embodiment, theunilateral shape similarity of solid hemisphere 1400 with respect tosolid hemisphere 1500 is ≈0.985, and the unilateral shape similarity ofsolid hemisphere 1500 with respect to solid hemisphere 1400 is ≈0.993.

The bilateral shape similarity operation is commutative:aΔb=bΔa  (Eq. 16)

By definition, the bilateral shape similarity of a Δ a=1, and the rangeof values of bilateral shape similarity is:0<aΔb≤1  (Eq. 17)It will be clear to those skilled in the art, after reading thisdisclosure, how to calculate (analytically or numerically) or determineempirically, the unilateral shape similarity of any two articles ofmanufacture. In accordance with the illustrative embodiment, thebilateral shape similarity of solid hemisphere 1400 and solid hemisphere1500 equals ≈0.989, as shown in Table 7.

Embodiments of the present invention are particularly useful formanufacturing operations in which the articles of manufacture arefabricated in large numbers and where the articles, as fabricated, havesimilar, but not identical, dimensions (e.g., articles of manufacturethat have bilateral shape similarity in the range of 0.98≤a Δ b<0.995).The reason is that embodiments of the present invention are most usefulwhen the dimensions of the articles are dissimilar.

Also at the end of task 1103 (after material has been removed as part ofthe process of embedding the representative fiducial marks)hemispherical shell 1600 and hemispherical shell 1700 have similar (butdifferent) volumes, similar (but different) masses, and similar (butdifferent) shapes. The volume, mass, and shape similarity ofhemispherical shell 1600 and hemispherical shell 1700 are presented inTable 8.

TABLE 8 Volume, Mass, and Shape Similarity of Hemispherical Shell 1600and Hemispherical Shell 1700 Unilateral Bilateral Article of Shape ShapeManufacture Volume Mass Similarity Similarity Hemispherical ≈422 cm³≈549 gr ≈0.991 ≈0.990 Shell 1600 Hemispherical ≈418 cm³  ≈2543 gr ≈0.989Shell 1700

In accordance with the illustrative embodiment, the unilateral shapesimilarity of solid hemisphere 1600 with respect to solid hemisphere1700 is ≈0.991. In accordance with the illustrative embodiment, theunilateral shape similarity of solid hemisphere 1700 with respect tosolid hemisphere 1600 is ≈0.989.

It will be clear to those skilled in the art, after reading thisdisclosure, how to accomplished task 1103.

FIG. 25 depicts a flowchart of the salient tasks associated with theperformance of task 1104—locating the first article of manufacture andthe second article of manufacture based on their representative fiducialmarks.

At task 2501, registration system 200 locates the first fiducialreference point in the article of manufacture by probing, with a probe,the hole comprising the representative fiducial mark.

Registration system 200 probes, with conical probe 256, the hole insolid hemisphere 1400 associated with fiducial reference point 1201-1until conical probe 256 fits—both laterally and angularly—the tangibleconical surface created in task 2401. This enables registration system200 to locate the first conical apex (i.e., the location of fiducialreference point 1201-1).

Registration system 200 probes, with conical probe 256, the hole insolid hemisphere 1500 associated with fiducial reference point 1201-1until conical probe 256 fits—both laterally and angularly—the tangibleconical surface created in task 2401. This enables registration system200 to locate the first conical apex (i.e., the location of fiducialreference point 1201-1).

Registration system 200 probes, with conical probe 256, the hole inhemispherical shell 1600 associated with fiducial reference point 1301-1until conical probe 256 fits—both laterally and angularly—the tangibleconical surface created in task 2401. This enables registration system200 to locate the first conical apex (i.e., the location of fiducialreference point 1301-1).

Registration system 200 probes, with conical probe 256, the hole inhemispherical shell 1700 associated with fiducial reference point 1301-1until conical probe 256 fits—both laterally and angularly—the tangibleconical surface created in task 2401. This enables registration system200 to locate the first conical apex (i.e., the location of fiducialreference point 1301-1).

At task 2502, registration system 200 locates the second fiducialreference point in the article of manufacture by probing, with a probe,the hole comprising the representative fiducial mark.

Registration system 200 probes, with conical probe 256, the hole insolid hemisphere 1400 associated with fiducial reference point 1201-2until conical probe 256 fits—both laterally and angularly—the tangibleconical surface created in task 2402. This enables registration system200 to locate the second conical apex (i.e., the location of fiducialreference point 1201-2).

Registration system 200 probes, with conical probe 256, the hole insolid hemisphere 1500 associated with fiducial reference point 1201-2until conical probe 256 fits—both laterally and angularly—the tangibleconical surface created in task 2402. This enables registration system200 to locate the second conical apex (i.e., the location of fiducialreference point 1201-2).

Registration system 200 probes, with conical probe 256, the hole inhemispherical shell 1600 associated with fiducial reference point 1301-2until conical probe 256 fits—both laterally and angularly—the tangibleconical surface created in task 2402. This enables registration system200 to locate the second conical apex (i.e., the location of fiducialreference point 1301-2).

Registration system 200 probes, with conical probe 256, the hole inhemispherical shell 1700 associated with fiducial reference point 1301-2until conical probe 256 fits—both laterally and angularly—the tangibleconical surface created in task 2402. This enables registration system200 to locate the second conical apex (i.e., the location of fiducialreference point 1301-2).

At task 2503, registration system 200 locates the third fiducialreference point in the article of manufacture by probing, with a probe,the hole comprising the representative fiducial mark.

Registration system 200 probes, with conical probe 256, the hole insolid hemisphere 1400 associated with fiducial reference point 1201-3until conical probe 256 fits—both laterally and angularly—the tangibleconical surface created in task 2403. This enables registration system200 to locate the third conical apex (i.e., the location of fiducialreference point 1201-3).

Registration system 200 probes, with conical probe 256, the hole insolid hemisphere 1500 associated with fiducial reference point 1201-3until conical probe 256 fits—both laterally and angularly—the tangibleconical surface created in task 2403. This enables registration system200 to locate the third conical apex (i.e., the location of fiducialreference point 1201-3).

Registration system 200 probes, with conical probe 256, the hole inhemispherical shell 1600 associated with fiducial reference point 1301-3until conical probe 256 fits—both laterally and angularly—the tangibleconical surface created in task 2403. This enables registration system200 to locate the third conical apex (i.e., the location of fiducialreference point 1301-3).

Registration system 200 probes, with conical probe 256, the hole inhemispherical shell 1700 associated with fiducial reference point 1301-3until conical probe 256 fits—both laterally and angularly—the tangibleconical surface created in task 2403. This enables registration system200 to locate the third conical apex (i.e., the location of fiducialreference point 1301-3).

At task 2504, registration system 200 locates the fourth fiducialreference point in the article of manufacture by probing, with a probe,the hole comprising the representative fiducial mark.

Registration system 200 probes, with conical probe 256, the hole insolid hemisphere 1400 associated with fiducial reference point 1201-4until conical probe 256 fits—both laterally and angularly—the tangibleconical surface created in task 2404. This enables registration system200 to locate the fourth conical apex (i.e., the location of fiducialreference point 1201-4).

Registration system 200 probes, with conical probe 256, the hole insolid hemisphere 1500 associated with fiducial reference point 1201-4until conical probe 256 fits—both laterally and angularly—the tangibleconical surface created in task 2404. This enables registration system200 to locate the fourth conical apex (i.e., the location of fiducialreference point 1201-4).

Registration system 200 probes, with conical probe 256, the hole inhemispherical shell 1600 associated with fiducial reference point 1301-4until conical probe 256 fits—both laterally and angularly—the tangibleconical surface created in task 2404. This enables registration system200 to locate the fourth conical apex (i.e., the location of fiducialreference point 1301-4).

Registration system 200 probes, with conical probe 256, the hole inhemispherical shell 1700 associated with fiducial reference point 1301-4until conical probe 256 fits—both laterally and angularly—the tangibleconical surface created in task 2404. This enables registration system200 to locate the fourth conical apex (i.e., the location of fiducialreference point 1301-4).

It will be clear to those skilled in the art, after reading thisdisclosure, how to accomplished task 1104.

What is claimed is:
 1. An article of manufacture comprising: a firsthole in a first portion of a material composing the article ofmanufacture, wherein the first hole in the first portion of the materialis defined, at least in part, by a first portion of a first tangibleconical surface, wherein the first tangible conical surface establishes(i) a first conical apex, and (ii) a first conical-surface volume; asecond hole in a second portion of the material composing the article ofmanufacture, wherein the second hole in the second portion of thematerial is defined, at least in part, by a second portion of a secondtangible conical surface, wherein the second tangible conical surfaceestablishes (i) a second conical apex, and (ii) a second conical-surfacevolume; and a third hole in a third portion of the material composingthe article of manufacture, wherein the third hole in the third portionof the material is defined, at least in part, by a third portion of athird tangible conical surface, wherein the third tangible conicalsurface establishes (i) a third conical apex, and (ii) a thirdconical-surface volume; wherein the first conical apex, the secondconical apex, and the third conical apex are non-collinear; and whereinthe first conical-surface volume does not equal the secondconical-surface volume; and wherein the first hole is a through hole;and wherein the second hole is a blind hole.
 2. The article ofmanufacture of claim 1: wherein the second conical-surface volume doesnot equal the third conical-surface volume; and wherein the firstconical-surface volume does not equal the third conical-surface volume.3. The article of manufacture of claim 1: wherein the first tangibleconical surface also establishes (iii) a first conical axis; wherein thesecond tangible conical surface also establishes (iii) a second conicalaxis; and wherein the first conical axis and the second conical axis arenon-parallel.
 4. The article of manufacture of claim 3 wherein the firstconical axis and the second conical axis are skew.
 5. The article ofmanufacture of claim 3: wherein the third tangible conical surface alsoestablishes (iii) a third conical axis; wherein the first conical axisand the third conical axis are non-parallel; and wherein the secondconical axis and the third conical axis are non-parallel.
 6. The articleof manufacture of claim 1 further comprising: a fourth hole in a fourthportion of the material composing the article of manufacture, whereinthe fourth hole is defined, at least in part, by a fourth portion of afourth tangible conical surface, wherein the fourth tangible conicalsurface defines a fourth conical apex; and wherein the first conicalapex, the second conical apex, the third conical apex, and the fourthconical apex are non-coplanar.
 7. The article of manufacture of claim 1:wherein the third hole in the third portion of the material is a blindhole.
 8. The article of manufacture of claim 1: wherein the third holein the third portion of the material is a through hole.
 9. The articleof manufacture of claim 1: wherein the first tangible conical surfacealso establishes (iii) a first conical-surface area; wherein the secondtangible conical surface also establishes (iii) a second conical-surfacearea; and wherein the first conical-surface area does not equal thesecond conical-surface area.
 10. The article of manufacture of claim 1:wherein the third tangible conical surface also establishes (iii) athird conical-surface area; wherein the first conical-surface area doesnot equal the third conical-surface area; and wherein the firstconical-surface area does not equal the second conical-surface area. 11.An article of manufacture comprising: a first hole in a first portion ofa material composing the article of manufacture, wherein the first holein the first portion of the material is defined, at least in part, by afirst portion of a first tangible conical surface, wherein the firsttangible conical surface establishes (i) a first conical apex, and (ii)a first conical axis; a second hole in a second portion of the materialcomposing the article of manufacture, wherein the second hole in thesecond portion of the material is defined, at least in part, by a secondportion of a second tangible conical surface, wherein the secondtangible conical surface establishes (i) a second conical apex, and (ii)a second conical axis; and a third hole in a third portion of thematerial composing the article of manufacture, wherein the third hole inthe third portion of the material is defined, at least in part, by athird portion of a third tangible conical surface, wherein theestablishes (i) a third conical apex, and (ii) a third conical axis;wherein the first conical apex, the second conical apex, and the thirdconical apex are non-collinear; and wherein the first conical axis andthe second conical axis are non-parallel; and wherein the first hole isa through hole; and wherein the second hole is a blind hole.
 12. Thearticle of manufacture of claim 11: wherein the first conical axis andthe third conical axis are non-parallel; and wherein the second conicalaxis and the third conical axis are non-parallel.
 13. The article ofmanufacture of claim 11 wherein the first conical axis and the secondconical axis are skew.
 14. The article of manufacture of claim 11wherein: wherein the first tangible conical surface also establishes(iii) a first conical-surface volume; wherein the second tangibleconical surface also establishes (iii) a second conical-surface volume;and wherein the first conical-surface volume does not equal the secondconical-surface volume.
 15. The article of manufacture of claim 14:wherein the third tangible conical surface also establishes (iii) athird conical-surface volume; wherein the second conical-surface volumedoes not equal the third conical-surface volume; and wherein the firstconical-surface volume does not equal the third conical-surface volume.16. The article of manufacture of claim 11 further comprising: a fourthhole in a fourth portion of the material composing the article ofmanufacture, wherein the fourth hole is defined, at least in part, by afourth portion of a fourth tangible conical surface, wherein the fourthtangible conical surface defines a fourth conical apex; and wherein thefirst conical apex, the second conical apex, the third conical apex, andthe fourth conical apex are non-coplanar.
 17. The article of manufactureof claim 11: wherein the third hole in the third portion of the materialis a blind hole.
 18. The article of manufacture of claim 11: wherein thethird hole in the third portion of the material is a through hole. 19.The article of manufacture of claim 11: wherein the first tangibleconical surface also establishes (iii) a first conical-surface area;wherein the second tangible conical surface also establishes (iii) asecond conical-surface area; and wherein the first conical-surface areadoes not equal the second conical-surface area.
 20. The article ofmanufacture of claim 11: wherein the third tangible conical surface alsoestablishes (iii) a third conical-surface area; wherein the firstconical-surface area does not equal the third conical-surface area; andwherein the first conical-surface area does not equal the secondconical-surface area.